EXAMPLE 3 Standardized Test Practice SOLUTION

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Presentation transcript:

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.

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 72.25 for A, x for d1, and 2x for d2.

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

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.

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 = 60 – 10 = 50 m

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)(40 + 70) = 2750 The area of the park is 2750 square meters. ANSWER

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

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