This document discusses finding the areas of triangles and trapezoids using formulas. It provides examples of calculating areas of various triangles and trapezoids by substituting values into the area formulas. It also includes an example calculating the approximate area of the state of Wisconsin by treating it as a trapezoid.

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

2. Warm Up
Evaluate.
24
19.44
68
Course 2
9-4 Area of Triangles and Trapezoids
1
2 · 6 · 8
1
2
· 5.4 · 7.2
3. 4(7 + 10)
4. 3.5(12 + 8.2)
1.
70.7
2.

3. Problem of the Day
(5.5)(1.5) = 8.25 in2
Course 2
9-4 Area of Triangles and Trapezoids
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.

4. Learn to find the area of triangles and
trapezoids.
Area of Triangles and Trapezoids
Course 2
9-4 Area of Triangles and Trapezoids

5. Course 2
9-4 Area of Triangles and Trapezoids
AREA OF A TRIANGLE
h
b
A =1
2
bh
The area A of a triangle
is half the product of its
base b and its height h.

6. Find the area of the triangle.
Additional Example 1A: Finding the Area of a
Triangle
Course 2
9-4 Area of Triangles and Trapezoids
5
8
A =
1
2
bh Use the formula.
A =
1
2
(8 · 5) Substitute 8 for b and
5 for h.
A = 20
The area of the triangle is 20 square units.

7. Find the area of the triangle.
Additional Example 1B: Finding the Area of a
Triangle
Course 2
9-4 Area of Triangles and Trapezoids
9
A =1
2
bh Use the formula.
A =1
2
(9 · 12) Substitute 9 for b and
12 for h.
A = 54
The area of the triangle is 54
square units.
12

8. Find the area of the triangle.
Course 2
9-4 Area of Triangles and Trapezoids
A =
1
2
bh Use the formula.
A =
1
2
(6 · 9) Substitute 6 for b and
9 for h.
A = 27
The area of the triangle is 27 square units.
Check It Out: Example 1A
6
9

9. Find the area of the triangle.
Course 2
9-4 Area of Triangles and Trapezoids
A =
1
2
bh Use the formula.
A =
1
2
(7 · 10) Substitute 7 for b and
10 for h.
A = 35
The area of the triangle is 35 square units.
Check It Out: Example 1B
10
7

10. 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.
h
b1
b2

11. Course 2
9-4 Area of Triangles and Trapezoids
AREA OF A TRAPEZOID
h
b1
A = 1
2
h(b1 + b2)
The area of a trapezoid
is half its height
multiplied by the sum of
its two bases.
b2
In the term b1, the number 1 is called a
subscript. It is read as “b-one” or “b sub-one.”
Reading Math

12. Find the area of the trapezoid.
Additional Example 2A: Finding the Area of a
Trapezoid
Course 2
9-4 Area of Triangles and Trapezoids
5 in.
6 in.
9 in.
A =1
2
h(b1 + b2) Use the formula.
A = 1
2
· 6(5 + 9)
A =1
2
· 6(14)
A = 42
The area of the trapezoid is 42 in2
.
Substitute.
Multiply.
Add.

13. Find the area of the trapezoid.
Additional Example 2B: Finding the Area of a
Trapezoid
Course 2
9-4 Area of Triangles and Trapezoids
A =1
2
h(b1 + b2) Use the formula.
A = 1
2
· 7(12 + 16)
A =1
2
· 7(28)
A = 98
The area of the trapezoid is 98 cm2
.
Substitute.
Multiply.
Add.
12 cm
16 cm
7 cm

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

15. Find the area of the trapezoid.
Course 2
9-4 Area of Triangles and Trapezoids
A =1
2
h(b1 + b2) Use the formula.
A = 1
2
· 9(5 + 16)
A =1
2
· 9(21)
A = 94.5
The area of the trapezoid is 94.5 cm2
.
Substitute.
Multiply.
Add.
Check It Out: Example 2B
16 cm
5 cm
9 cm

16. The state of Wisconsin is shaped somewhat
like a trapezoid. What is the approximate area
of the state?
Additional Example 3: Geometry Application
Course 2
9-4 Area of Triangles and Trapezoids
A =1
2
h(b1 + b2) Use the formula.
A = 1
2
· 300(153 + 220)
A =1
2
· 300(373)
A = 55,950
The area of Wisconsin is approximately
56,000 square miles.
Substitute.
Multiply.
Add.

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

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