1. Objective: To find the area of a trapezoid, kite and a rhombus.
Chapter 7 Lesson 4
Objective: To find the area of a trapezoid, kite and a rhombus.

2. height of a trapezoid: the perpendicular distance h between the bases.
Leg
Leg h b2
Base
Theorem7-10: Area of a Trapezoid The area of a trapezoid is half the product of the height and the sum of the bases. b1 h b2

3. Example 1: Find Area of a Trapezoid
Find the area of a trapezoid with height 7 cm and bases 12 cm and 15 cm.

4. Example 2: Find Area of a Trapezoid
Find the area of a trapezoid with height 18 cm and bases 20 cm and 36 cm.

5. Example 3: Finding Area Using a Right Triangle
Find the area of the trapezoid. Leave your answer in simplest radical form.
5cm
5cm
Since you do not have the height of the trapezoid we will have to draw it in. h
60°
7cm
2cm
5cm
Find h.
Find area.

6. Example 4: Finding Area Using a Right Triangle
Find the area of the trapezoid. Leave your answer in simplest radical form.
11cm
Since you do not have the height of the trapezoid we will have to draw it in. h
60°
5cm
16cm
11cm
Find h.
Find area.

7. Theorem 7-11: Area of a Rhombus or a Kite
The area of a rhombus or a kite is half the product of the lengths of its diagonals. d2 d1
Rhombuses and kites have perpendicular diagonals.

8. Finding the Area of a Kite
Example 5:
Finding the Area of a Kite
Find the area of kite KLMN. L
KM=2+5=7
LN=3+3=6 3m 2m K M 5m 3m N

9. Finding the Area of a Kite
Example 6:
Finding the Area of a Kite
Find the area of kite KLMN. L
KM=1+4=5
LN=3+3=6 3m 1m K M 4m 3m N

10. Finding the Area of a Kite
Example 7:
Finding the Area of a Kite
Find the area of kite with diagonals that are 12 in. and 9 in. long.

11. Example 8: The diagonals of a rhombus bisect each other.
Finding the Area of a Rhombus B
15m
Find the area of rhombus ABCD.
∆BEC is a right triangle. Use the Pythagorean Theorem to find BE. E A C
12m
AC=12+12=24
BD=9+9=18 D

12. Finding the Area of a Rhombus
Example 9:
Finding the Area of a Rhombus B
13m
Find the area of rhombus ABCD.
∆BEC is a right triangle. Use the Pythagorean Theorem to find BE.
24m E A C
12m
12m
AC=12+12=24
BD=5+5=10 D

13. Assignment
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