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Objective
Find the area of complex figures
Vocabulary
Complex figure
A figure that is made up of two or more shapes
Example 1 Find the Area of a Complex Figure
Example 2 Find the Area of a Complex Figure
Find the area of the complex figure.
Triangle
Rectangle
2
1
3
Triangle
Identify each shape in the figure
Find the area of each shape
then add the areas together!
Muy facil!
1/2
Find the area of the complex figure.
1
2
3
A = 5 in2
Write formula for area of triangle
Replace b with 5
Replace h with 2
Multiply
1/2
Find the area of the complex figure.
1
Triangle 1: A = 5 in2
2
Triangle 3: A = 5 in2
3
Triangle 3 has the same
measurements of triangle 1 so
area will be the same
Find area of rectangle
1/2
Find the area of the complex figure.
1
Triangle 1: A = 5 in2
2
Triangle 3: A = 5 in2
A=LW
A=7 5
A = 35
3
in2
Write formula for area of rectangle
Replace L with 7
Replace W with 5
Multiply
1/2
Find the area of the complex figure.
1
Triangle 1: A = 5 in2
2
Triangle 3: A = 5 in2
Rectangle: A = 35 in2
Answer:
Total Area = 45 in2
3
Add the 3 areas together
1/2
Find the area of the complex figure.
Answer:
1/2
Find the area of the complex figure.
Semi-circle
Rectangle
Semi-circle
1
2
3
Identify each shape in the figure
Find the area of each shape
then add the areas together!
2/2
Find the area of the complex figure.
1
2
3
Write formula for area of a circle
Remember: it is a semi-circle so
divide the area by 2 or multiply
by ½
Replace r with 3
Remember: radius is half the
diameter
2/2
Find the area of the complex figure.
1
2
Follow Order of Operations
P
E
MD
AS
9
A = 14.14
cm2
Find 32
Multiply
2/2
3
Find the area of the complex figure.
Semi-Circle 1:
A = 14.14 cm2
Semi-Circle 3:
A = 14.14 cm2
1
2
3
Semi-Circle 3 has the same
measurements of Semi-Circle 1
so area will be the same
Find area of rectangle
2/2
Find the area of the complex figure.
Semi-Circle 1:
A = 14.13 cm2
Semi-Circle 3:
A = 14.13 cm2
1
2
3
A=LW
Write formula for area of rectangle
A = 12  6
Replace L with 12
A = 72
cm2
Replace W with 6
Multiply
2/2
Find the area of the complex figure.
Semi-Circle 1:
A = 14.13 cm2
Semi-Circle 3:
A = 14.13 cm2
Rectangle 2:
A = 72 cm2
Answer:
Total Area = 100.28 cm2
1
2
Add the 3 areas together
2/2
3
Find the area of the complex figure. Round to the
nearest hundredth.
Answer:
15.57 ft2
2/2
Assignment
Lesson 7:3
Area of Complex Figures
3 - 13 All
Below are plans for the new deck on the Obwena’s house.
How many square feet of wood will be needed if one
square represents two square feet?
3:3
SHORT-RESPONSE TEST ITEM Below are plans for
the new deck on the Obwena’s house. How many
square feet of wood will be needed if one square
represents two square feet?
Read the Test Item
You need to find the area
of the deck in square
units and then multiply
this result by 2 to find the
area of the deck in square
feet.
3:3
Solve the Test Item
Find the area of the deck by dividing it into smaller areas.
2:3
Region A
Square
or 4
Region B
Triangle
or 2
Region C
Rectangle
or 6
2:3
Region D
Rectangle
or 8
Region E
Triangle
Region F
Rectangle
2:3
Region G
Triangle
Region H
Square
2:3
Add areas:
Area = A + B + C + D + E + F + G + H
Area = 4 + 2 + 6 + 8 + 4 + 6 + 2 + 4
Area = 36 feet2
Multiply by 2 since each square
on the deck plan equals 2 feet2
36  2
Answer:
Deck = 72 feet2
2:3
*
SHORT-RESPONSE TEST ITEM Below are plans for
the new patio to be added in the Murphy’s back yard.
How many square feet of concrete will need to be
poured if one square represents two square feet?
Answer:
2:3