As shown in the right figure, in the trapezoidal ABCD, AD / / BC, the area of triangle Abe is 30 square centimeters, EC = 2ae, calculate the area of trapezoidal ABCD The figure is trapezoid with two diagonals The order is (from left to right) ADB The focus is e

As shown in the right figure, in the trapezoidal ABCD, AD / / BC, the area of triangle Abe is 30 square centimeters, EC = 2ae, calculate the area of trapezoidal ABCD The figure is trapezoid with two diagonals The order is (from left to right) ADB The focus is e

S (triangle BEC): s (triangle ABE) = EC: AE = 2
S (triangle BEC) = 2S (triangle ABE) = 2 * 30 = 60
S (triangle ADE): s (triangle BEC) = (AE / EC) ^ 2 = (1 / 2) ^ 2 = 1 / 4
S (triangle BEC) = 4S (triangle ADE)
S (triangle ADE) = 1 / 4S (triangle BEC) = 1 / 4 * 60 = 15
S (triangle DEC): s (triangle ADE) = EC: AE = 2
S (triangle DEC) = 2S (triangle ADE) = 2 * 15 = 30
S (trapezoidal ABCD) = the sum of the areas of four triangles = 15 + 30 + 30 + 60 = 135