1. Area of Triangles and Trapezoids
8-5
Area of Triangles and Trapezoids
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Area of Triangles and Trapezoids
Course 2
8-5
Area of Triangles and Trapezoids
Warm Up
Evaluate. 1 2 1.
· 6 · 8 24 2. 1 2
· 5.4 · 7.2
19.44
3. 4(7 + 10) 68
( )
70.7

3. Area of Triangles and Trapezoids
Course 2
8-5
Area of Triangles and Trapezoids
Problem of the Day
4 in.
1.5 in.
7 in.
An isosceles trapezoid has bases of 7 in. and 4 in. and height 1.5 in. Find its area by using only the formula for the area of a parallelogram.
(5.5)(1.5) = 8.25 in2

4. Area of Triangles and Trapezoids Area of Triangles and Trapezoids
Course 2
8-5
Area of Triangles and Trapezoids
Area of Triangles and Trapezoids
Learn to find the area of triangles and trapezoids.

5. Area of Triangles and Trapezoids
Course 2
8-5
Area of Triangles and Trapezoids
A diagonal of a parallelogram divides the parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram.
Height
Height
Base
Base
The base of a triangle can be any side. The height of a triangle is the perpendicular distance from the base to the opposite vertex.

6. Area of Triangles and Trapezoids
Course 2
8-5
Area of Triangles and Trapezoids
AREA OF A TRIANGLE
The area A of a triangle
is half the product of its
base b and its height h. 1 2
A = bh h b

7. Additional Example 1A: Finding the Area of a Triangle
Course 2
8-5
Areas of Triangles and Trapezoids
Additional Example 1A: Finding the Area of a Triangle
Find the area of the triangle. A. 1 2
A = bh
Use the formula. 5 1 2
Substitute 8 for b and
5 for h.
A =
(8 · 5) 8
A = 20
The area of the triangle is 20 square units.

8. Additional Example 1B: Finding the area of a Triangle
Course 2
8-5
Area of Triangles and Trapezoids
Additional Example 1B: Finding the area of a Triangle
Find the area of the triangle. B. 1 2
A = bh
Use the formula. 12 1 2
A =
(9 · 12)
Substitute 9 for b and
12 for h. 9
A = 54
The area of the triangle is 54 square units.

9. Areas of Triangles and Trapezoids
Course 2
8-5
Areas of Triangles and Trapezoids
Try This: Example 1A
Find the area of the triangle. A. 1 2
A = bh
Use the formula. 1 2
Substitute 6 for b and
9 for h.
A =
(6 · 9) 9
A = 27 6
The area of the triangle is 27 square units.

10. Areas of Triangles and Trapezoids
Course 2
8-5
Areas of Triangles and Trapezoids
Try This: Example 1B
Find the area of the triangle. B. 1 2
A = bh
Use the formula. 1 2
Substitute 7 for b and
10 for h. 10
A =
(7 · 10)
A = 35 7
The area of the triangle is 35 square units.

11. Area of Triangles and Trapezoids
Course 2
8-5
Area of Triangles and Trapezoids
A parallelogram can be divided into two congruent trapezoids. The area of each trapezoid is one-half the area of the parallelogram. 1 2
Area of a trapezoid =
(base of
parallelogram)(height).

12. Area of Triangles and Trapezoids
Course 2
8-5
Area of Triangles and Trapezoids
The two parallel sides of a trapezoid are its bases. If we call the longer side b1 and the shorter side b2, then the base of the parallelogram is b1 + b2. 1 2
Area of a trapezoid =
(base 1 +
base 2)(height).

13. Area of Triangles and Trapezoids
Course 2
8-5
Area of Triangles and Trapezoids
AREA OF A TRAPEZOID b2
The area of a trapezoid is half its height multiplied by the sum of its two bases. 1 2 A =
h(b1 + b2) h b1

14. Additional Example 2A: Finding the Area of a Trapezoid
Course 2
8-5
Areas of Triangles and Trapezoids
Additional Example 2A: Finding the Area of a Trapezoid
Find the area of the trapezoid. A.
5 in. 1 2
A =
h(b1 + b2)
Use the formula. 1 2
A =
· 6(5 + 9)
6 in.
Substitute. 1 2
A =
· 6(14)
Add.
9 in.
A = 42
Multiply.
The area of the trapezoid is 42 in2.

15. Additional Example 2B: Finding the Area of a Trapezoid
Course 2
8-5
Areas of Triangles and Trapezoids
Additional Example 2B: Finding the Area of a Trapezoid
Find the area of the trapezoid. B. 1 2
12 cm
A =
h(b1 + b2)
Use the formula. 1 2
A =
· 7( )
7 cm
Substitute. 1 2
Add.
A =
· 7(28)
16 cm
A = 98
Multiply.
The area of the trapezoid is 98 cm2.

16. Areas of Triangles and Trapezoids
Course 2
8-5
Areas of Triangles and Trapezoids
Try This: Example 2A
Find the area of the trapezoid. A. 1 2
A =
h(b1 + b2)
Use the formula. 1 2
A =
· 6(11 + 4)
Substitute.
11 in.
4 in.
6 in. 1 2
Add.
A =
· 6(15)
A = 45
Multiply.
The area of the trapezoid is 45 in2.

17. Areas of Triangles and Trapezoids
Course 2
8-5
Areas of Triangles and Trapezoids
Try This: Example 2B
Find the area of the trapezoid. B. 1 2
A =
h(b1 + b2)
Use the formula.
16 cm 1 2
A =
· 9(5 + 16)
Substitute.
9 cm 1 2
Add.
5 cm
A =
· 9(21)
A = 94.5
Multiply.
The area of the trapezoid is 94.5 cm2.

18. Area of Triangles and Trapezoids Insert Lesson Title Here
Course 2
8-5
Area of Triangles and Trapezoids
Insert Lesson Title Here
Lesson Quiz
Find the area of each figure. 1. 3.
9 in2 2.
45 ft2
3 in.
9 ft
6 in.
10 ft
8 ft
10 ft 4.
87.5 ft2
60 ft2
7 ft
6 ft
15 ft
12 ft
4. What is the height of a triangle with area 36 cm2 and a base 9 cm?
8 cm