1. LESSON 7.4
AREAS OF TRAPEZOIDS, RHOMBUSES, AND KITES
OBJECTIVE:
To find the areas of trapezoid,
rhombuses, and kites

2. Theorem 7-10 Area of a Trapezoid The area of a trapezoid is
one-half the product of the height
and the sum of the bases. b2 b1 h
A = ½ h( b1 + b2)

3. The height (h) of a trapezoid is
the  distance between the two bases.

4. lengths of the diagonals.
Theorem 7-1: Area of a Rhombus or a kite
The area of a rhombus or kite is
half the product of the
lengths of the diagonals.
A = ½d1d2

5. A rhombus is also a
parallelogram. We will
use A = bh most of the time.
Reminder:

6. Find the area of trapezoid ABCD.
Example #1
Find the area of trapezoid ABCD.
(Show formula, substitution, & simplify.)
5 ft.
12 ft. A B C D
11 ft.

7. A = ½ h( b1 + b2) A = ½ (12)( 11 + 16) A = (6)( 27) A = 162 ft2 11 ft.C D
11 ft.
A = ½ (12)( )
A = (6)( 27)
A = 162 ft2

8. A car window is shaped like the trapezoid shown. If the area of the
Example #2
A car window is shaped like the
trapezoid shown. If the area of the
window is 504 in2find the measure of
the missing base. Show all steps.
20 in.
18 in.

9. A = ½ h( b1 + b2) 504 = ½ (18)( 20 + b2) 504 = (9)(20 + b2)
20 in.
18 in.
504 = ½ (18)( 20 + b2)
504 = (9)(20 + b2)
56 = 20 + b2
36 in. = b2

10. Find the area of kite WXYZ.
Example #3
Find the area of kite WXYZ.
d2 = = 5
d1 = = 6 W X Y Z
3 cm
4 cm
1 cm

11. W X Y Z
3 cm
4 cm
1 cm
A = ½ d1d2
A = ½(6)(5)
A = 15 cm2

12. Example #4
If the area of rhombus RSTU is 120 ft2, then find the measure of the missing diagonal.
24 ft. U R S T

13. A = ½ d1d2
24 ft. U R S T
120 = ½(24)d2
120 = 12d2
10 ft = d2

14. ASSIGNMENT:
Worksheet 7.4
Min. 3 lines per problem
plus units