The perimeter of rectangle ABCD is 30 cm, where BE: EC = 3: 2; ECDK is a square. Calculate the area of the AECD shape.

univerkov | June 15, 2021 | education

The AECD figure is a trapezoid. Its area can be found by the formula: half the sum of the bases, multiplied by the height. The bases of the trapezoid are EC and AD, and the height is CD.

Hence, Saesd = (EC + AD) / 2 * CD.

Since BE: EC = 3: 2, let BE = 3x, EC = 2x. Then BC = 3x + 2x = 5x.

CD = EC = 2x (since ECDK is a square).

It turns out that the perimeter of the ABCD rectangle is 5x + 2x + 5x + 2x = 30 cm.

Hence, 14x = 30; x = 30/14 = 15/7.

EC = 2x = 2 * 15/7 = 30/7.

AD = BC = 3x + 2x = 5x = 5 * 15/5 = 75/7.

CD = EC = 30/7.

We substitute everything into the formula for finding the area of a trapezoid:

S = (30/7 + 75/7): 2 * 30/7 = 105/7 * 1/2 * 30/7 = 3150/98 = 225/7 = 32 1/7 cm ^ 2.

Answer: the area of the AECD is 32 1/7 cm ^ 2.

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