Perimeter, Area and Volume
Grades F to A
Hyperlinks!
Counting Squares
Area – working
backwardsCircles
Volume of cuboids
Sectors of circlesSurface area
Volume of prisms
Volume and surface area of complex
shapes
Rectangles and Triangles
Parallelograms and
Trapeziums
Compound Shapes
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Area and perimeter by counting and measuring
How do I find the area and perimeter of a shape?
Grade F
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
What are perimeter and area?
Perimeter is the length around the outside of a shape.
Area is the space inside a shape.
Example
The rectangle has a perimeter of:
The rectangle has a area of:
5 + 3 5 + 3+ = 16cm
5 × 3 = 15cm²
5 + 5 = 15cm²5 +Take note of
the units!
Find the perimeter and area of this rectangle:
Perimeter =
Area =
20cm
24cm²
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Rectangles and Triangles
Can I calculate the perimeter and area of a rectangle and triangle?
Grade E
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
The formulae to remember:•
Two examples:Example 1
Find the area and perimeter of this rectangle:
Area = 8 × 6Area = 48cm²
Perimeter = 8 + 6 + 8 + 6Perimeter = 28cm
Example 2Find the area of this triangle:
Area = 5 × 12 ÷ 2Area = 60cm² ÷ 2
Area = 30cm²
6cm
8cm
5cm13cm
12cm
Have a go at some:Question 1
Find the area of this triangle:Question 2
Find the perimeter and area of this rectangle:
10cm
11cm
8cm7cm
Answer: 35cm²Answer:
Area = 88cm²Perimeter = 38cm
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Parallelograms and Trapeziums
Can I calculate the area of a parallelogram and trapezium?
Grade D
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
The formulae:•
Two examplesExample 1
Find the area of this parallelogram:
Area = 7 × 5Area = 35cm²
Example 2
•
7cm
5cm 6cm 5cm
4cm
8cm
Have a go at a couple of questions:Question 1
Find the area of this parallelogram:
Question 2
Find the area of this trapezium:
12cm
8cm10cm 7cm
9cm
11cm
Answer: 96cm²Answer: 70cm²
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Circles
Can I find the circumference and area of a circle?
Grade C
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Names to do with circles you must remember:
Radius
Diameter
Chord
Tangent
Circumference
Formulae you need to remember:
•
A couple of examplesExample 1
Find the circumference and area of a circle with a diameter
of 10cm to 1 dp.
Circumference = π × 10Circumference = 31.4cm
Area = π × 5²Area = 78.5cm²
Example 2Find the circumference and
area of a circle with a radius of 8cm to 1 dp.
Circumference = π × 16Circumference = 50.3cm
Area = π × 8²Area = 201.1cm²
Some for you to try:Question 1
Find the circumference and area of this circle to 1 dp.
Question 2Find the circumference and
area of a circular pond with a diameter of 3m to 1 dp.
Circumference = 88.0cmArea = 615.8cm²
Circumference = 9.4mArea = 7.1m²
14cm
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Area – Working Backwards
Now you can find the area of shapes, can you find a length having been
given the area?
Formulae Reminder:•
Find the missing lengths:
Area = 48cm²Area = 21cm²
Area = 32cm² Area = 28cm² Area = 113.1cm²
8cm
?cm 7cm
?cm
8cm
9cm
?cm
Diameter = ?Height = ? Height = 4cm
None of these are drawn to
scale
6cm
6cm
4cm
5cm
12cm
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Compound Shapes
Can I calculate the perimeter and area of a compound shape?
Grade C
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
What is a compound shape?
A compound shape is a shape that is made up of lots of different shapes.
The key is to split the complex shape up into simpler shapes, find the areas of the simple
shapes then add your areas together.
An exampleFind the area of this shape:
Split it up!
Area = 40 + 32 = 72cm²
12cm
8cm8cm
3cm
Area = 8×5 = 40cm²Area = 8×4
= 32cm²
Another exampleFind the area of this shape:
Split it up!
Area = 54 + 13.5 = 67.5cm²
3m
9m
6m Area = 9×6 = 54m²
A couple of questions:Question 1
Find the area of this shape:
Question 2
Find the area of this shape:
10m
8m
6cm
12cm
3cm
5cm
Answer: 66cm² Answer: 119.3m²
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Volume of Cuboids
Can I calculate the volume of a cuboid?Grade C
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
How to calculate the volume of a cuboid:
•
An example:Find the volume of this cuboid:
Volume = 3 × 5 × 4Volume = 60cm³
3cm
5cm4cm
Take note of the units!
Another example, working backwards:
Find the height of this cuboid:
280cm³ = 10 × 7 × hh = 280 ÷ (10 × 7)
h = 4cm
10cm7cm
Volume = 280cm³
Two questions to have a go at:
Question 1Find the volume of this cuboid:
Question 2The tank below contains exactly 100 litres of water. How far up the tank does the water go?
(Hint: 1 litre = 1000cm³)
5cm
8cm
6cm
1m0.5m
0.5m
Answer: 240cm³ Answer: 0.2m or 20cm
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Prisms
Can I calculate the volume of a prism?
Grade C
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
What is a prism?
A prism is a 3D shape that has the same cross-section all the way through.
For example:
Triangular Prism Hexagonal Prism Cylinder
Calculating the volume of a prism:
Find the area of the cross-section then multiply by the length.
Volume = Area of cross-section × length
Two examplesExample 1
•
Example 2
If the volume of this prism is 360cm³ and it is 9cm long,
what is the area of the cross-section?
Area of cross-section = 360 ÷ 9Area of cross-section = 40cm²
8cm
3cm
A couple of questions:Question 1
Find the volume of this triangular prism:
Question 2A circular pond contains
18,850 litres of water. It has a diameter of 4m. How deep is
the pond if it is a cylinder?(1 litre = 1000cm³)
8cm 12cm
9cm
Answer: 432cm³ Answer: 1.5m or 150cm
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Surface Area
Can I calculate the surface area of a cuboid or a triangular prism?
Grade C to B
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
What is surface area?
The area of all the faces of a 3D shape added together.
You could think of it like this: it is the exact amount of wrapping paper you would need to
wrap your shape up with.
Find the surface area of this cuboid:
Each face you can see has a face exactly the same opposite it.
2 × 4 × 10 = 80cm²2 × 4 × 5 = 40cm²
2 × 5 × 10 = 100cm²Total surface area = 220cm²
4cm
10cm5cm
4cm × 5cm = 20cm²5cm × 10cm = 50cm²
4cm × 10cm = 40cm²
There are two of each size of
rectangle
Find the surface area of these two cuboids:
Cuboid 1
Answer: 258cm²
Cuboid 2
Answer: 192cm²
9cm
5cm6cm
4cm
12cm3cm
A Triangular Prism Example:•
A Cylinder Example:Find the surface area of this cylinder:
It’s two circles and a rectangle (whose length is the circumference of the circle):
Surface area = 2 × π × 4² + 5 × π × 8
Surface area = 226.2cm²
4cm5cm
The two circles The rectangle
Find the surface area:
Answer: 527.8cm²
12cm
8cm
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Sectors of Circles
Can I find the area of a sector and its arc length?
Grade B
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
What is a sector?
A sector is a fraction of a circle – like a slice of cake or pizza.
It’s point is the centre of the circle.
The arc length is the curved part of the sector.
The formulae:•
Area of a whole circle
Circumference of a whole circle
Angle given for the sector
An exampleFind the area and arc length of this sector.
7cm
7cm50
Area:
Area = 21.4cm²
Arc Length:
Arc Length = 44.1cm
A question for you:Find the area and perimeter of this sector.
(Don’t forget the “straight bits” for the perimeter!)
Area = 15.4cm² Perimeter = 15.7cm
4cm4cm 110
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Volume and Surface Area of Complex Shapes
Can I use the formulae to find surface area and volume of cones and
spheres?Grade A
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
Some formulae for you:
• •
These formulae are at the front of the paper!
And one more…
•
Cone Example:• •
5cm
12cm 13cm
Circular base
Curved surface area
Sphere Example:
• •
r = 6cm
Two questionsQuestion 1
Find the volume and curved surface area of this cone:
Question 2
Find the volume and curved surface area of this sphere:
6cm
8cm 8cm
C.S.A. = 188.5cm² Volume = 301.6cm³
Surface area = 804.2cm² Volume = 2144.6cm³
The frustumA frustum is a cone or pyramid that has had it’s
top chopped off!
Remember: the original cone/pyramid and the cone/pyramid that has been chopped off are similar, mean that the dimensions are in the
same ratio.
Find the volume of the frustum:•
3cm
6cm
5cmDouble the radius, so
double the height
Try this one:
Find the volume of this frustum:
3cm
9cm
8cm
Answer: 980.2cm³
Success Criteria: Where Are We Now?Level Learning outcomes: R A G
F2 I can find the perimeter and area on a shape by measuring or counting.
E3 I can find the perimeter and area of a triangles and quadrilaterals by calculation.
D1 I can find the area of a parallelogram and trapezium. C3 I can find the circumference and area of a circle. C3 I can find the area of a compound shape. C3 I can calculate the volume of a cuboid. C2 I can find the volume of a prism, including a cylinder. C1 I can calculate the surface area of a prism. B1 I can find the area and perimeter of sectors of circles. A2 I can calculate the volume and surface area of non-prisms
such as cones and spheres using the formulae.
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