The bases of an isosceles trapezoid have lengths that differ by 30. The two legs of the trapezoid
have length 28, and the two diagonals of the trapezoid have length 52. What is the area of the
trapezoid?
The bases of an isosceles trapezoid have lengths that differ by 30. The two legs of the trapezoid have a length of 28, and the two diagonals of the trapezoid have a length of 52. What is the area of the trapezoid?
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Height h = sqrt(282 - 152)
Shorter Base SB = sqrt(522 - h2) - 15
Longer Base LB = SB + 30
Trapezoid area A = 1/2 (SB + LB) * h
Let the shorter base = B
Let the longer base = B + 30
1/2 the difference in the bases = (B + 30 - B) /2 = 15
We can find the height of the trapezoid as sqrt ( 28^2 - 15^2) = sqrt (559)
And we can find the length of the shorter base as
sqrt [ 52^2 - (15+ B)^2] = sqrt (559)
2704 - B^2 - 30B - 225 = 559
B^2 - 30B - 1920 = 0
B = sqrt (2145 ) - 15
And the longer base = sqrt (2145) + 15
Area = (1/2) sqrt (559) ( 2sqrt (2145) ) = sqrt (559) sqrt (2145) ≈ 1095 units^2