1. Areas of Trapezoids, Rhombuses, and Kites
Warm Up
Lesson Presentation
Lesson Quiz

2. Warm-Up
1. Find the area of a parallelogram with height 12 feet
and base 8 feet.
ANSWER
96 ft2
2. Find the area of an isosceles triangle with sides 20,
20, and 24 units.
ANSWER
192 square units

3. Warm-Up
3. What is the length of the midsegment of a trapezoid
with bases 10 inches and 15 inches?
ANSWER
12.5 in.
4. Solve 200 = 1 2 x
( ).
ANSWER 10

4. Example 1
The free-throw lane on an international basketball court is shaped like a trapezoid. Find the area of the free-throw lane.
BASKETBALL

5. The area of the free-throw lane is about 27.8 square meters.
Example 1
SOLUTION
The height of the trapezoid is 5.8 meters. The lengths of the bases are 3.6 meters and 6 meters.
A = h(b1 + b2) 1 2
Formula for area of a trapezoid
= (5.8)( ) 1 2
Substitute 5.8 for h, 3.6 for b1, and
6 for b2. =
Simplify.
The area of the free-throw lane is about 27.8 square meters.

6. Example 2
Rhombus PQRS represents one of the inlays on a guitar. Find the area of the inlay.
MUSIC
SOLUTION
STEP 1
Find the length of each diagonal. The diagonals of a rhombus bisect each other, so QN = NS and PN = NR.
QS = QN + NS = = 18 mm
PR = PN + NR = = 24 mm

7. Find the area of the rhombus. Let d1 represent QS and d2 represent PR.
Example 2
STEP 2
Find the area of the rhombus. Let d1 represent QS and d2 represent PR.
A = d1d2 1 2
Formula for area of a rhombus
= (18)(24) 1 2
Substitute.
= 216
Simplify.
The area of the inlay is 216 square millimeters.

8. Guided Practice
Find the area of the figure. 1.
28 ft2
ANSWER

9. Guided Practice
Find the area of the figure. 2.
42 in.2
ANSWER

10. Guided Practice
Find the area of the figure. 3.
2400 m2
ANSWER

11. Example 3
SOLUTION
Draw and label a diagram. Let x be the length of one diagonal. The other diagonal is twice as long, so label it 2x. Use the formula for the area of a kite to find the value of x.

12. The lengths of the diagonals are 8.5 inches and 2(8.5) = 17 inches.
Example 3
A = d1d2 1 2
Formula for area of a kite
72.25 = (x)(2x) 1 2
Substitute for A, x for d1,
and 2x for d2.
72.25 = x2
Simplify.
Find the positive square root of
each side.
8.5 = x
The lengths of the diagonals are 8.5 inches and
2(8.5) = 17 inches.
The correct answer is C.
ANSWER

13. Example 4
You have a map of a city park. Each grid square represents a 10 meter by 10 meter square. Find the area of the park.
City Planning

14. Example 4
SOLUTION
STEP 1
Find the lengths of the bases and the height of trapezoid ABCD.
b1 = BC = 70 – 30
= 40 m
b2 = AD = 80 – 10
= 70 m
h = BE = – 10
= 50 m
STEP 2
Find the area of ABCD.
A = h(b1 + b2) 1 2 1 2 =
(50)( )
= 2750
The area of the park is 2750 square meters.

15. Guided Practice
4. The area of a kite is 80 square feet. One diagonal is 4 times as long as the other. Find the diagonal lengths.
d1 = 2 √10 ft, d2 = 8 √10 ft
ANSWER
5. Find the area of a rhombus with vertices M(1, 3), N(5, 5), P(9, 3), and Q(5, 1).
16 units2
ANSWER

16. Lesson Quiz
Find the area of each figure. 1.
ANSWER
20 square units

17. Lesson Quiz
Find the area of each figure. 2.
ANSWER
144 cm2

18. Lesson Quiz
Find the area of each figure. 3.
ANSWER
135 ft2

19. Lesson Quiz
Find the area of each figure. 4.
ANSWER
1072 ft2

20. Lesson Quiz
5. The height of a trapezoid is 8 feet. One base is
twice as long as the other, and the area is 72
square feet. How long is each base?
ANSWER
6 ft; 12 ft