The area of the parallelogram ABCD is 176. Point E is the middle of the side AD. Find the area of the trapezoid AECB

bystudin | May 31, 2020 | Education

Draw the height of the parallelogram DO, as shown in the figure. The area of the parallelogram is equal to the product of the side by the height of the parallelogram.
S parallelogram = BC * h = 176
And the area of the trapezoid is equal to the product of half the sum of the bases by height.
Straps = h * (BC + AE) / 2.
AE = AD / 2 (by the condition of the problem).
AD = BC (according to the parallelogram property).
Therefore, AE = BC / 2.
Then S trapezoid = h * (BC + BC / 2) / 2 = h * (3 * BC / 2) / 2 = h * 3 * BC / 4 = h * BC * 3/4 = S paralma * 3 / 4 = 176 * 3/4 = 132.
Answer: S trapezoid = 132

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