1. Area of Triangles and Trapezoids
10-2
Area of Triangles and Trapezoids
Course 1
Warm Up
Problem of the Day
Lesson Presentation

2. Warm Up
Evaluate.
1. If the height of a rectangle equals the base of a parallelogram and the base of the rectangle equals the height of the parallelogram, then the rectangle and the parallelogram have the same area.
2. Find the area of a rectangle with a length of 53 in. and a width of 47 in.
True
2,491 in2

3. Which is a better deal, 3 discs for $5.00 or 4 discs for $7.00?
Problem of the Day
Which is a better deal, 3 discs for $5.00 or 4 discs for $7.00?
3/$5.00

4. Learn to find the area of triangles and trapezoids.

5. You can divide any parallelogram into two congruent triangles
You can divide any parallelogram into two congruent triangles. So the area of each triangle is half the area of the parallelogram.
Height
Height
Base
Base

6. 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
Find the area of the triangle. 1 2
A = bh
Write the formula. 1 2
Substitute 20 for b and 12 for h.
A =
(20 · 12) 1 2
A =
(240)
Multiply.
A = 120
The area is 120 ft2.

8. The legs of a triangle must meet at a 90◦ angle in order to use their lengths as the base and height of the triangle.
Caution!

9. Additional Example 1B: Finding the Area of a Triangle
Find the area of the triangle. 1 2
A = bh
Write the formula. 1 2
Substitute 30 for b and 24 for h.
A =
(30 · 24) 1 2
A =
(720)
Multiply.
A = 360
The area is 360 in2.

10. Find the area of the triangle.
Check It Out: Example 1A
Find the area of the triangle. 1 2
A = bh
Write the formula. 1 2
Substitute 5 for b and 8 for h.
A =
(5 · 8)
8 in. 1 2
5 in.
A =
(40)
Multiply.
A = 20
The area is 20 in2.

11. Find the area of the triangle.
Check It Out: Example 1B
Find the area of the triangle. 1 2
A = bh
Write the formula.
A = 1 2
(4 • 24)
Substitute 4 for b and 24 for h. 1 2
24 ft 1 2
A =
(108)
Multiply.
4 ft 1 2
A = 54
The area is 54 in2.

12. Additional Example 2: Application
The diagram shows the section of a forest being studied. What is the area of the section? 1 2
A = bh
Write the formula. 1 2
Substitute 43.9 for b. Substitute 16 for h.
A =
(43.9 • 16) 1 2
A =
(702.4)
Multiply.
A = 351.2
The area is km2.

13. Substitute 48 for b. Substitute 24.5 for h. A = (48 · 24.5)
Check It Out: Example 2
The diagram shows the section of a park being studied. What is the area of the section?
24.5 m
48 m 1 2
A = bh
Write the formula. 1 2
Substitute 48 for b. Substitute 24.5 for h.
A =
(48 · 24.5) 1 2
A =
(1176)
Multiply.
A = 588
The area is 588 m2.

14. AREA OF A TRAPEZOID b2
The area of a trapezoid is the product of half its height and the sum of its bases. 1 2 A =
h(b1 + b2) h b1

15. Additional Example 3: Finding the Area of a Trapezoid
Find the area of the trapezoid. 1 2
A =
h(b1 + b2)
Use the formula.
A = 1 2
· 4( )
Substitute 4 for h, 14 for b1, and for b2. 1 2
A = 1 2
· 4(26 )
A = 53
Multiply.
The area is 53 yd2.

16. Find the area of the trapezoid.
Check It Out: Example 3
12 cm
Find the area of the trapezoid.
7 cm
16 cm 1 2
A =
h(b1 + b2)
Use the formula. 1 2
Substitute 7 for h, 16 for b1, and 12 for b2.
A =
· 7( ) 1 2
A =
· 7(28)
A = 98
Multiply.
The area is 98 cm2.

17. Lesson Quiz
Find the area of each triangle. 1. 3.
39.9 cm2 2.
84 mi2
Find the area of each trapezoid.
3 4
22.5 m2 4.
113 in2