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Transcript of 2D Geometry Part 2: Area - content.njctl.orgcontent.njctl.org/courses/math/archived-courses... ·...
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2D Geometry Part 2:Area
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Table of Contents
TrianglesTrapezoidsCircles
Irregular Shapes
Rectangles Click on a topic to go to that sectionParallelograms
Shaded Regions
Mixed Review
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Area - The number of square units (units2) it takes to cover the surface of a figure.
ALWAYS label units2!!!
12 ft
6 ft
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How many 1 ft2 tiles does it take to cover the rectangle?
Use the squares to find out!
Look for a faster way than covering the whole figure.
12 ft
6 ft
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A = length(width)A = lw
A = side(side)A = s2
The Area (A) of a rectangle is found by using the formula:
The Area (A) of a square is found by using the formula:
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1 What is the Area (A) of the figure?
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15 ft
6 ft
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2 Find the area of the figure below.
7
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3 Dr. Dan wants to keep his kitten from running through his flower bed by putting up some fencing. The flower bed is 10 ft. by 6ft. Will Dr. Dan need to know the area or the perimeter of his flower bed to keep his kitty from trampling the flowers?
A AreaB Perimeter
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4 Now solve the problem....
Dr. Dan wants to keep his kitten from running through his flower bed by putting up some fencing. The flower bed is 10 ft. by 6ft. How much fencing will he need?
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Area of a Parallelogram
Let's use the same process as we did for the rectangle. How many 1 ft2 tiles fit across the bottom of the parallelogram?
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Area of a Parallelogram.
Let's use the same process as we did for the rectangle. If we build the parallelogram with rows of 14 ft2, what happens?
How tall is the parallelogram?How can you tell?
14 ft
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How does this help us find the area of the parallelogram?
14 ft
How do you find the area of a parallelogram?
5 ft
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A = base(height)A = bh
The Area (A) of a parallelogram is found by using the formula:
Note: The base & height always form a right angle!
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Example.
Find the area of the figure.
4 cm
4 cm
2.2 cm 2.2 cm1.9 cm
click to reveal
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Try These.
Find the area of the figures.
8
75
click to reveal
11 m
click to reveal
14 m
11 m
20 m
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5 Find the area.
11 ft 10 ft
12 ft
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6 Find the area.
17 in
17 in
10 in 12 in
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12 in
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7 Find the area.
7 m
13 m 13 m
7 m
11 m
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8 Find the area.
12 cm
11 cm
9 cm
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Area of a Triangle
Let's use the same process as we did for the rectangle & parallelogram. How many 1 ft2 tiles fit across the bottom of the triangle?
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Area of a Triangle
If we continue to build the triangle with rows of 10 ft2, what happens?
How tall is the triangle? How can you tell?
10 ft
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How does this help us find the area of the triangle?
14 ft
See that the rectangle we built is twice as large as the triangle. How do you find the area of a triangle?
10 ft
4 ft
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Is this true for all triangles?Let's see!
Calculating base(height) results in 2 triangles!
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The Area (A) of a triangle is found by using the formula:
Note: The base & height always form a right angle!
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Example.
Find the area of the figure.
4 cm
10 cm 10 cm
6 cm
click to reveal
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Try These.
Find the area of the figures.
13 ft
11 ft
9 ft 12 ft 1420
16
15
click to reveal
click to reveal
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9 Find the area.
8 in
5 in
11 in 10 in
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10 Find the area
15 m
8 m9 m 12 m
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Area of a Trapezoid
· Cut the trapezoid in half horizontally· Rotate the top half so it lies next to the bottom half· A parallelogram is created
See the diagrams below
Base1
Base2
Height
Base1Base2
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The Area (A) of a trapezoid is found by using the formula:
Note: The base & height always form a right angle!
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Example.
Find the area of the figure.
12 cm
10 cm 11 cm
9 cm
click to reveal
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Try These.
Find the area of the figures.
13 ft
11 ft
9 ft 11 ft
20
15
click to reveal
11 ft
click to reveal
9 117
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11 Find the area of the trapezoid.
4 m
10 m
6.5 m
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12 Find the area of the trapezoid.
22 cm
14 cm
8 cm
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Area of a Circle
The Area (A) of a Circle is found by solving the following formula:
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7 cm
Find the area of the circle.A = # r2
1. Substitute the radius into formula.A = # (7)2
2. Use 3.14 as an approximation for # .A = 3.14(49)A = 153.86 cm2
3. Don't forget to label the units as square units.
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13 What is the Area (A) of a Circle with a radius (r) of 8 m?
8 m
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14 What is the Area (A) of the circle?
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15 What is the Area (A) of the circle?
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16 A circular sprinkler sprays water with a radius of 11 ft. How much area can the sprinkler cover?
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17 What is the area of a circle with a diameter of 24 yds?
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18 What is the radius of a circle whose area is 254.34 mm2?
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19 A circular pool has an area of 153.86 ft2.What is its diameter?
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20 Find the perimeter of the figure.
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4 cm 3 cm 4 cm
11 cm
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21 Find the area of the figure.
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4 yd
8 yd
9 yd
8 yd
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22 Find the perimeter of the figure.
4 m
7 m
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23 Find the circumference of the figure.
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12 in
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24 Find the area of the figure.
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9 in 5 in
12 in
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25 Find the area of the figure.
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4 cm 3 cm 4 cm
11 cm
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26 Find the perimeter of the figure.
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9 in 5 in
12 in
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27 Find the perimeter of the figure.
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4 yd
8 yd
9 yd
8 yd
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28 Find the area of the figure.
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12 in
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29 Find the area of the figure.
4 m
7 m
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Area of Irregular FiguresMethod #1
1. Divide the figure into smaller figures (that you know how to find the area of)
2. Label each small figure and find the area of each
3. Add the areas
4. Label your answer
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Example:Find the area of the figure.
10 m
6 m
3 m2 m
10 m
6 m
3 m2 m #1
#2
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Area of Irregular FiguresMethod #2
1. Create one large, closed figure.
2. Label the small added figure and find the area.
3. Find the area of the new, large figure
4. Subtract the areas
5. Label your answer
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Example:Find the area of the figure.
10 m
6 m
3 m2 m
10 m
6 m
3 m2 m
Whole Rectangle
Extra Rectangle
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Try These:Find the area of each figure.
2m
4m
2m5m
20 ft
16 ft
8 ft
10 ft
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30 Find the area.
4'
2.5'
1.5'
2.5'
8.75'
7.75'
5.25'
Top Rectangle
Bottom Rectangle
Vertical Rectangle
Total Area
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31 Find the area.Whole New Figure
New Rectangle
Total Area
16
121925
35
13
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32 Find the area.Triangle
Rectangle
Total Area
8 cm 58 cm
15 cm
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33 Find the area.
4 ft.
9 ft.
5 ft.
6 ft.
Side Rectangle
Bottom Right Rectangle
Total Area
Half Circle
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Area of a Shaded Region
1. Find area of whole figure.
2. Find area of unshaded figure(s).
3. Subtract unshaded area from whole figure.
4. Label answer with units2
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Example
Find the area of the shaded region.
15 ft
20 ft
7 ft7 ft
Area Whole Rectangle
Area Unshaded Square
Area Shaded Region
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Try This
Find the area of the shaded region.Area Whole Square
Area Circle
Area Shaded Region14 cm
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Try This
Find the area of the shaded region. Area Trapezoid
Area Rectangle
Area Shaded Region
20 m
12 m3 m
8 m2 m
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34 Find the area of the shaded region.
6'
8'
2'4'
Area Whole Rectangle
Area Unshaded
Area Shaded Region
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35 Find the area of the shaded region.
11"
12"
8"7"
6"
Area Parallelogram
Area Triangle
Area Shaded Region
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12"
14"
8"
6"
8"
4"
36 Find the area of the shaded region.
Area Whole
Area Rectangle
Area Shaded Region
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37 Find the area of the shaded region.
Area Circle
Area Triangle
Area Shaded Region
4 yd
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38 A cement path 3 feet wide is poured around a rectangular pool. If the pool is 15 feet by 7 feet, how much cement was needed to create the path?
Area Path & Pool
Area Pool
Area Path
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