Measuring area & volume © 2013 Meredith S. Moody 1.

GeometryMeasuring area & volume

© 2013 Meredith S. Moody 1

Objective: You will be able to…

Find length, area, and volume measurements for basic polyhedrons


Vocabulary

Length: For a 1-dimensional figure, the number of units from one end of the figure to the other


Finding length

Decide what tool is appropriate

Measure to the appropriate degree of accuracy

Record your measurement in the appropriate units


Finding length: Example


The crayon measures ~ 2.8 inchesThe pencil measures ~ 15.9 centimeters

Finding length: You tryUsing the appropriate tool, measure the length of three different items in the room

Record your measurements using the appropriate units


Vocabulary

Area: For a 2-dimensional figure, the number of square units that figure covers

For quadrilaterals, counting these square units is easy


Area of rectangles: Example

Rectangles are quadrilaterals

Here, a rectangle takes up 18 square units.

These units might be inches, centimeters, or even miles

Because it is rectangular, instead of counting, you can use multiplication (which is repeated addition)


Area of rectangles: You tryUsing the appropriate measurement

tool, measure 2 different rectangles in the room

Record your measurements in square units For example, your desktop might be 18

inches long and 20 inches wide, so 18 in. x 20 in. = 360 square inches


Area of parallelogramsParallelograms are also

quadrilateralsYou can think of a parallelogram

as a transformed rectangleThe area of a parallelogram is

still the number of square units it covers


Area of parallelogram: Example

Once your parallelogram becomes a rectangle, you can easily measure the area using the previous steps


Area of parallelograms: You try Find the area of

the given parallelogram

Once you convert the parallelogram to a rectangle, it is easy to see that the shape takes up 40 square units, or 5 x 8


Area of triangles What is the

relationship between a triangle and a square?

If you can find the area of a square, you can use it to find the area of a triangle


Area of triangles

You can find the area (A) of a triangle more quickly by using a formula that is based on the rule that a triangle is half of a rectangle

A(triangle) = ½ (base x height)


Area of trianglesThe height of a triangle is always

perpendicular to its base (90˚)


Area of triangles: Example What is the area of

the pictured triangle?

The base = 8cm The height =

5cm 8 x 5 = 40 40 ÷ 2 = 20 The area of this

triangle = 20 cm²


6cm

Area of triangles: You try! What is the area of

the given triangle? base = 12 in. height = 8 in. 12 x 8 = 96 96 ÷ 2 = 48 area = 48 in.²


Vocabulary

Surface area: For a 3-dimensional figure, the sum of the surface area measurements of all the sides of the figure


Surface area: Cubes To find the surface

area of a cube (3-dimensional quadrilateral), you must find the area of each surface and then add them together


Cube

Surface area: Cubes If all the surfaces are the same size (have

the same area), you can use multiplication (repeated addition) to find the surface area more quickly


Surface area: Cubes You try! Find the surface area

of the given cube (all sides are equal lengths)

The area of each side is 3x3=9 square ft

There are 6 sides: 9 x 6 = 54

Surface area = 54 ft²


3 ft.

Surface area: Other solids

You can find the surface area of any 3-dimensional shape by measuring the area of all its surfaces and then finding the sum


Vocabulary

Volume: For a 3-dimensional figure, the number of cubic units that will fit inside the figure


Finding volume

For a 3-dimensional quadrilateral, find the length and width and height and multiply them all together

Your result will be cubic units (i.e. 9 cubic inches…in.³)


Example: Volume What is the

volume of the pictured solid?

The solid is 2 units wide, 3 units long, and 5 units high

We could count all the units, but multiplying is faster


Finding volume: You try!

What is the volume of the pictured solid?

4cm x 3cm x 5cm = 60 cm³ The solid can hold

60 cubic centimeters


You try!Measure the length of a pencil Decide what measuring tool to use▪ ruler

Decide what units to use▪ Inches or centimeters

Measure to the appropriate degree of accuracy


You try!

Measure the area of a textbook cover Measure the length Measure the width Multiply them together Report your measurement in

square units


You try!

Find the volume of a rectangular prism Measure the length Measure the width Measure the height Multiply them all together Report your measurement in cubic

units© 2013 Meredith S. Moody 29

Class work

Work with a partner to measure 10 items in the classroom – you must have at least 1 length, 1 area, and 1 volume measurement

Remember to record your measurements in square or cubic units when appropriate!


Measuring area & volume © 2013 Meredith S. Moody 1.

Documents

Transcript of Measuring area & volume © 2013 Meredith S. Moody 1.