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EXAMPLE 3

Standardized Test Practice. 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 2 x . Use the formula for the area of a kite to find the value of x . 1. A = d 1 d 2. 2. 1.

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EXAMPLE 3

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  1. Standardized Test Practice EXAMPLE 3 SOLUTION Draw and label a diagram. Let xbe 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. 1 A = d1d2 2 1 72.25 = (x)(2x) 2 Standardized Test Practice EXAMPLE 3 Formula for area of a kite Substitute72.25for A, xfor d1, and2xford2.

  3. ANSWER The correct answer is C. Standardized Test Practice EXAMPLE 3 72.25 = x2 Simplify. 8.5 = x Find the positive square root of each side. The lengths of the diagonals are8.5 inches and 2(8.5) = 17 inches.

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

  5. b1 = BC = 70 – 30 b2 = AD = 80 – 10 h = BE = 60 – 10 Find an area in the coordinate plane EXAMPLE 4 SOLUTION STEP 1 Find the lengths of the bases and the height of trapezoid ABCD. = 40 m = 70 m = 50 m

  6. 1 1 A = h(b1 + b2) = (50)(40 + 70) 2 2 ANSWER The area of the park is 2750square meters. Find an area in the coordinate plane EXAMPLE 4 STEP 2 Find the area of ABCD. = 2750

  7. Draw and label a diagram. Let xbe the length of one diagonal. The other diagonal is 4 times as long, so label it 4x. Use the formula for the area of a kite to find the value of x. 4x x for Examples 3 and 4 GUIDED PRACTICE 4. The area of a kite is 80square feet. One diagonal is 4 times as long as the other. Find the diagonal lengths. SOLUTION

  8. 1 A = d1d2 2 1 80 = (x(4x)) 2 2√ 10 = x The lengths of the diagonals ared1 = 2 √10 ft d2= 4(2 √ 10 ) = 8 √10 ft. ANSWER for Examples 3 and 4 GUIDED PRACTICE Formula for area of a kite Substitute so forA, xfor d1, and4xford2. 80 = 2 x2 Simplify. Find the positive square root of each other.

  9. for Examples 3 and 4 GUIDED PRACTICE 5. Find the area of a rhombus with vertices M(1, 3), N(5, 5), P(9, 3), andQ(5, 1). SOLUTION N P M Q STEP 1 Find the lengths of the diagonals (MP, NQ) of the rhombus MNPQ.

  10. d1 = NP d2 = NQ = 9– 1 = 5 –1 1 1 A = b1 b2 = 8 4 2 2 ANSWER The area of the rhombus MNPQ is 16units2. for Examples 3 and 4 GUIDED PRACTICE = 8 = 4 Find the area of MNPQ. STEP 2 = 16 units2.

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