In the trapezoid ABCD with bases AD = 11cm, BC = 7cm, a segment ВM is drawn. M belongs to AD

univerkov | May 7, 2021 | education

In the trapezoid ABCD with bases AD = 11cm, BC = 7cm, a segment ВM is drawn. M belongs to AD, parallel to CD sotrona. S (BCDM) = 35 cm2. Find: S (ABCD).

Consider a quadrangle MBCD, in which, by condition, BM is parallel to CD, and BC is parallel to MD as the base of the trapezoid, then the quadrilateral is a parallelogram.

Let us omit the height CH from the top of the trapezoid.

The parallelogram area is equal to: Smvsd = BC * CH = 7 * CH = 35 cm2.

Then CH = 35/7 = 5 cm.

Determine the area of the trapezoid.

Savsd = (AD + BC) * CH / 2 = (11 + 7) * 5/2 = 45 cm2.

Answer: Savsd = 45 cm2.

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