Area and Perimeter

1
Area and Perimeter

• Review

2
Area Formula Review
Area Parallelogram (rectangle, rhombus, and
square)
Area - Triangle
Area - Square
3
Formulas
Area of a circle
Circumference of a circle
Area - Trapezoid
4
Area of a Triangle

• Area equals the base times the height divided by
  2.
• Find the area of triangle ABC

B
8 in
C
A
6 in
5
Practice

• Vicki wants to plant a flower garden with an area
  of 480 ft² with a height of 24ft. What will the
  base of that triangle be?

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Vicki wants to plant a flower garden with an area
of 480 ft² with a height of 24ft. What will the
base of that triangle be?

• Make an illustration
• Write down the formula A ½bh
• Substitute what we know into the formula
• 480ft² ½ (b)(24ft)
• Solve the equation algebraically

B
24 ft
A480 ft²
C
A
base
7
Vicki wants to plant a flower garden with an area
of 480 ft² with a height of 24ft. What will the
base of that triangle be?

• 480ft² ½ (b)(24ft)
• Multiply what you can
• 480ft² (b)(12ft)
• To isolate the variable perform the inverse
  operation

Vickis triangular flower garden has a base 40
feet in length.
B
24 ft
A480 ft²
C
A
base
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What is the area of parallelogram ABCD

• A bh
• A (12m)(9m)
• A 108m²

B
A
9m
C
D
12m
9
What is the height of parallelogram with a base
of 18ft and an area of 216ft²
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What is the height of parallelogram with a base
of 18ft and an area of 216ft²

• Draw the picture
• A bh
• substitute what you know
• 216ft² (18ft)x
• Solve for x

B
A
A 216ft²
x
C
D
18ft
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What is the height of parallelogram with a base
of 18ft and an area of 216ft²

• The height of the parallelogram is 12ft.

12
area of a trapezoid

• use the formula

3 ft.
B
C
2.5 ft.
A
D
4.5 ft.
13
3 ft.
B
C
2.5 ft.
A
D
4.5 ft.

• The area of this trapezoid is 9.375ft²

14
Using area of a trapezoid

• What is the height?

8 in.
B
C
A 36 in²
h
A
D
10 in.
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What is the height?

• The height of this trapezoid is 4 in.

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Isosceles Triangle

• A triangle where two sides are equal
• What is the area
• What is the perimeter

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Isosceles Triangle

• What is the area

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Isosceles Triangle

• What is the perimeter
• The height will cut the base exactly in half
• Two identical right triangles
• The height is a leg
• Half the base is the second leg

h 18 in.
14 in.
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Isosceles Triangle

• What is the perimeter
• Find the hypotenuse

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Isosceles Triangle

• What is the perimeter
• Find the hypotenuse
• a² b² c²

h 18 in.
c
c
18 in.
7 in.
7 in.
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Isosceles Triangle

• What is the perimeter
• P 19.31in. 19.31in. 14in.
• P 52.62in.

19.31in.
19.31in.
h 18 in.
18 in.
14 in.
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What is the area of a circle with a radius of 4cm?
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What is the circumference of a circle with a
radius of 6cm?
24

• Sam wants to paint his living room wall and does
  not know how much paint to purchase
• Sam drew a diagram of the wall
• Sam knows the paint he wants will cover 250 ft²
• How much paint should Sam purchase?

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area of an irregular polygon

• Separate it into its parts
• Find the area of each part
• Take the sum of the parts

13 ft.
13 ft.
8 ft.
38 ft.
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area of an irregular polygon

• First lets look at the rectangle
• A(38ft.)(8ft.)
• A304ft²

13 ft.
8 ft.
38 ft.
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area of an irregular polygon

• Now lets look at the triangle
• The base is 38ft
• The height is 13ft 8ft 5ft

13 ft.
8 ft.
38 ft.
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area of an irregular polygon
13 ft.
8 ft.
38 ft.
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area of an irregular polygon

• Find the sum of the two areas

13 ft.
8 ft.
Total Area 304ft² 95ft²
Total Area 399ft²
38 ft.
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area of an irregular polygon

• The area Sam is painting is 399ft²
• Divide the area by the number of square feet one
  gallon will cover.
• Sam will need to purchase 2 gallons of paint

Total Area 399ft²
8 ft.
38 ft.
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area of an irregular polygon

• Separate it into its parts
• Find the area of each part
• Take the sum of the parts