The area of the parallelogram ABCD is equal to 181 points e the middle of the side AD. Find the area of the trapezoid AECB.

univerkov | August 2, 2021 | education

To solve the problem, consider the figure.

From point E, which is the middle of AD, draw a line EK parallel to AB and CD.

The area of the parallelogram CDEK is equal to half the area of the parallelogram ABCD.

S cdek = 181/2 = 90.5 cm2.

EC is the diagonal of the parallelogram CDEK that bisects it. The area of the CKE triangle is equal to half the area of the CDEK parallelogram.

Scke = S cdek / 2 = 90.5 / 2 = 45.25 cm2.

Then the area of the trapezoid AECB is equal to: Saecb = S cdek + Scke = 90.5 + 45.25 = 135.75 cm2.

Answer: The area of the trapezoid is 135.75 cm2.

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