For this case we have: a = 30 cm c = 16 cm We look for the length of the diagonal: d = x + y Where, For x: a ^ 2 = x ^ 2 + x ^ 2 x = a / root (2) = 30 / root (2) = 21.2132 cm For y: c ^ 2 = y ^ 2 + y ^ 2 y = c / root (2) = 16 / root (2) = 11.3137 cm The diagonal is: d = x + y d = 21.2132 + 11.3137 d = 32.5269 cm Then, the height is: h = h1 + h2 For h1: h1 = root (x ^ 2 - (a / 2) ^ 2) = root ((21.2132) ^ 2 - (30/2) ^ 2) h1 = 15 cm For h2: h2 = root (y ^ 2 - (c / 2) ^ 2) = root ((11.3137) ^ 2 - (16/2) ^ 2) h2 = 8 cm Finally: h = h1 + h2 h = 15 + 8 h = 23 cm Then, the area is: A = (1/2) * (a + c) * (h) A = (1/2) * (30 + 16) * (23) A = 529 cm ^ 2 Answer: the area of an isosceles trapezoid is: A = 529 cm ^ 2
