1. Area of Triangles and Trapezoids
9-4
Area of Triangles and Trapezoids
Course 2
Warm Up
Problem of the Day
Lesson Presentation

2. Area of Triangles and Trapezoids
Course 2
9-4
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
9-4
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
9-4
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
9-4
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

6. Additional Example 1A: Finding the Area of a Triangle
Course 2
9-4
Area of Triangles and Trapezoids
Additional Example 1A: Finding the Area of a Triangle
Find the area of the triangle. 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.

7. Additional Example 1B: Finding the Area of a Triangle
Course 2
9-4
Area of Triangles and Trapezoids
Additional Example 1B: Finding the Area of a Triangle
Find the area of the triangle. 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.

8. Area of Triangles and Trapezoids
Course 2
9-4
Area of Triangles and Trapezoids
Check It Out: Example 1A
Find the area of the triangle. 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.

9. Area of Triangles and Trapezoids
Course 2
9-4
Area of Triangles and Trapezoids
Check It Out: Example 1B
Find the area of the triangle. 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.

10. Area of Triangles and Trapezoids
Course 2
9-4
Area of Triangles and Trapezoids
The two parallel sides of a trapezoid are its bases, b1 and b2. The height of a trapezoid is the perpendicular distance between the bases. b2 h b1

11. Area of Triangles and Trapezoids
Course 2
9-4
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
In the term b1, the number 1 is called a subscript. It is read as “b-one” or “b sub-one.”
Reading Math

12. Additional Example 2A: Finding the Area of a Trapezoid
Course 2
9-4
Area of Triangles and Trapezoids
Additional Example 2A: Finding the Area of a Trapezoid
Find the area of the trapezoid.
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.

13. Additional Example 2B: Finding the Area of a Trapezoid
Course 2
9-4
Area of Triangles and Trapezoids
Additional Example 2B: Finding the Area of a Trapezoid
Find the area of the trapezoid. 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.

14. Area of Triangles and Trapezoids
Course 2
9-4
Area of Triangles and Trapezoids
Check It Out: Example 2A
Find the area of the trapezoid. 1 2
A =
h(b1 + b2)
Use the formula. 1 2
A =
· 6(11 + 4)
Substitute.
11 in.
4 in.
6 in. 1 2
· 6(15)
Add.
A =
A = 45
Multiply.
The area of the trapezoid is 45 in2.

15. Area of Triangles and Trapezoids
Course 2
9-4
Area of Triangles and Trapezoids
Check It Out: Example 2B
Find the area of the trapezoid. 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.

16. Additional Example 3: Geometry Application
Course 2
9-4
Area of Triangles and Trapezoids
Additional Example 3: Geometry Application
The state of Wisconsin is shaped somewhat like a trapezoid. What is the approximate area of the state? 1 2
A =
h(b1 + b2)
Use the formula. 1 2
A =
· 300( )
Substitute. 1 2
A =
· 300(373)
Add.
A = 55,950
Multiply.
The area of Wisconsin is approximately 56,000 square miles.

17. Area of Triangles and Trapezoids
Course 2
9-4
Area of Triangles and Trapezoids
Check It Out: Example 3
A large preserve has a similar trapezoid shape. What is the approximate area of the preserve?
232 mi 1 2
A =
h(b1 + b2)
Use the formula.
129 mi 1 2
A =
· 129( )
Substitute.
116 mi 1 2
· 129(347)
Add.
A =
A = 22,446
Multiply.
The area of the preserve is approximately 22,446 square miles.

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