In trapezoid ABCD. AD 10 cm. BC 5 cm. Let’s draw a segment BM. M point belongs to AD

univerkov | September 8, 2021 | education

In trapezoid ABCD. AD 10 cm. BC 5 cm. Let’s draw a segment BM. M point belongs to AD parallel to the side of CD. Parallelogram area BCDM 25 cm2. Find the area of the trapezoid.

Since the BCDM is a parallelogram, its opposite sides are equal, therefore MD = BC = 5 cm.

Let us draw the height of CH from the vertex C of the trapezoid.

Let’s use the formula for the area of a parallelogram. Svsdm = MD * CH.

25 = MD * 5.

МD = 25/5 = 5cm.

Determine the area of the trapezium ABCD.

Savsd = (ВС + АD) * СН / 2 = (5 + 10) * 5/2 = 37.5 cm2.

Answer: Savsd = 37.5 cm2.

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