1. Area of Trapezoids

2. Goal
Find the area of trapezoids.

3. Key Vocabulary
Trapezoid
Base of a trapezoid
Height of a trapezoid

4. Trapezoid
A trapezoid is a quadrilateral with exactly one pair of parallel sides.
Each of the parallel sides is called a base.
The nonparallel sides are called legs.
Height of the trapezoid is the shortest distance (perpendicular distance) between the bases.

5. What is the area of this trapezoid?
Area of Trapezoid
b1=base 1
h=height
What is the area of this triangle?
What is the area of this trapezoid?
b2=base 2

6. What is the area of this trapezoid?
Area of Trapezoid
b1=base 1
h=height
What is the area of this trapezoid?
b2=base 2
COPY THIS!

7. What is the area of this trapezoid?
Area of Trapezoid
b1=base 1
h=height
What is the area of this trapezoid?
b2=base 2
PASTE HERE!

8. What is the area of this trapezoid?
Area of Trapezoid
b1=base 1
h=height
What is the area of this trapezoid?
b2=base 2
FLIP VERTICALLY!

9. What is the area of this trapezoid?
Area of Trapezoid
b1=base 1
h=height
What is the area of this trapezoid?
b2=base 2
FLIP HORIZONTALLY!

10. What is the area of this trapezoid?
Area of Trapezoid
b1=base 1
h=height
What is the area of this trapezoid?
b2=base 2
TRANSLATE TO HERE!

11. What is the area of this trapezoid?
Area of Trapezoid
b1=base 1
h=height
What is the area of this trapezoid?
b2=base 2
b1=base 1
CHECK MEASUREMENTS!

12. Area of the trapezoid is ½ the area of this parallelogram?
Area of Trapezoid
b1=base 1
Area of the trapezoid is ½ the area of this parallelogram?
h=height
b2=base 2
b1=base 1

13. Area of Trapezoid b1=base 1 h=height Areatrapezoid =
½ height(base 1 + base 2)
b2=base 2
b1=base 1

14. Areatrapezoid = ½ h(b1 + b2)
Area of Trapezoid
b1=base 1
h=height
Areatrapezoid = ½ h(b1 + b2)
b2=base 2
b1=base 1

15. Area of Trapezoid Words: Area = ½(height)(base1+base2)
Symbols: A = 1/2h(b1+b2)

16. Find the area of the trapezoid.
Example 1
Find the Area of a Trapezoid
Find the area of the trapezoid.
SOLUTION
Formula for the area of a triangle
A =
h(b1 + b2) 1 2 = 1 2
(5)(6 + 8)
Substitute 5 for h, 6 for b1, and 8 for b2. = 1 2
(5)(14)
Simplify within parentheses.
= 35
Simplify.
ANSWER
The area of the trapezoid is 35 square inches. 16

17. Your Turn:
Find the area of the trapezoid. 1.
ANSWER
63 m2 2.
ANSWER
182 ft2 3.
ANSWER
50 cm2

18. Example 2
Use the Area of a Trapezoid
Find the value of b2 given that the area of the trapezoid is 96 square meters.
SOLUTION
A = 1 2
h(b1 + b2)
Formula for the area of a trapezoid 1 2
(8)(9 + b2)
96 =
Substitute 96 for A, 8 for h, and 9 for b1.
192 = 8(9 + b2)
Multiply each side by 2.
192 = b2
Use the distributive property.
120 = 8b2
Subtract 72 from each side.
15 = b2
Divide each side by 8.
ANSWER
The value of b2 is 15 meters. 18

19. Your Turn:
A gives the area of the trapezoid. Find the missing measure. 1.
A = 77 ft2
ANSWER
h = 7 ft 2.
A = 39 cm2
ANSWER
b1 = 5 cm 3.
A = 84 in.2
ANSWER
b2 = 8 in.
A trapezoid has an area of 294 square yards. Its height is 14 yards and the length of one base is 30 yards. Find the length of the other base. 4.
ANSWER
12 yards

20. Assignment
Pg. 448 – 450: #1 – 15 odd, 19 – 37 odd