1. EXAMPLE 3
Standardized Test Practice
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.

2. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
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.

3. Standardized Test Practice
EXAMPLE 3
Standardized Test Practice
72.25 = x2
Simplify.
8.5 = x
Find the positive square root of
each side.
The lengths of the diagonals are 8.5 inches and
2(8.5) = 17 inches.
The correct answer is C.
ANSWER

4. EXAMPLE 4
Find an area in the coordinate plane
City Planning
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.

5. EXAMPLE 4
Find an area in the coordinate plane
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

6. EXAMPLE 4
Find an area in the coordinate plane
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.
ANSWER

7. GUIDED PRACTICE
for Examples 3 and 4
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

8. GUIDED PRACTICE
for Examples 3 and 4
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