1. Area of Triangles and Trapezoids
Course 2
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

2. Area of Triangles and Trapezoids
Course 2
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

3. Area of Triangles and Trapezoids Area of Triangles and Trapezoids
Course 2
Area of Triangles and Trapezoids
Area of Triangles and Trapezoids
Learn to find the area of triangles and trapezoids.

4. Area of Triangles and Trapezoids
Course 2
AF 3.1 Use variables in expressions describing geometric quantities.
-Objective :Students will use variables in expressions describing geometric quantities
for Areas of triangles and trapezoids by using equation formulas and scoring an 80% proficiency on an exit slip.

5. Area of Triangles and Trapezoids
Course 2
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
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
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
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
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
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
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
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
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
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. 84
A = 42
Multiply.
The area of the trapezoid is 42 in2.

15. Additional Example 2B: Finding the Area of a Trapezoid
Course 2
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
196
A = 98
Multiply.
The area of the trapezoid is 98 cm2.

16. Areas of Triangles and Trapezoids
Course 2
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
· 6(15)
Add.
A = 90
A = 45
Multiply.
The area of the trapezoid is 45 in2.

17. Areas of Triangles and Trapezoids
Course 2
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
· 9(21)
Add.
5 cm
A =
189
A = 94.5
Multiply.
The area of the trapezoid is 94.5 cm2.

18. Area of Triangles Exploration Activity
Cut out the pieces of the rectangle and the dotted rectangle
and glue each piece on your notebook.
2) Use the ruler to find the sides of the rectangle and triangles in inches.
(Find the Length and Width of the Rectangles and the Base and Height of
Each triangle)
3) Once you have all the measurements, find the AREA for each shape!
Use : A = L X W Use: (Base x Height) 1 2

19. Area of Triangles and Trapezoids Insert Lesson Title Here
Course 2
Area of Triangles and Trapezoids
Insert Lesson Title Here
Lesson Exit Slip
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

20. 5

22. 6