In the trapezoid ABCD of the base AD = 4; BC = 3, and its area is 84.

| July 5, 2021 | education

In the trapezoid ABCD of the base AD = 4; BC = 3, and its area is 84. Find the area of the trapezoid BCMN, where MN is the midline of the trapezoid ABCD.

Determine the length of the segment NM, which is the middle line of the trapezoid.

NM = (AD + DC) / 2 = (4 + 3) / 2 = 3.5 cm.

Let’s draw the height BH from point B of the trapezoid.

Knowing the area of the trapezoid and the middle line of the trapezoid, we determine the height BH.

S = NM * BH.

84 = 3.5 * BH.

BH = 84 / 3.5 = 24 cm.

Consider a triangle ABH, in which the angle H is straight, since BH is the height, the segments AN and NB are equal, since NM is the middle line of the trapezoid, NO is parallel to AH, and therefore NO is the middle line of the triangle ABH and then, BO = OH = BH / 2 = 24/2 = 12 cm.

Determine the area of the trapezoid BCMN.

Sbcmn = BO * (BC + MN) / 2 = 12 * (3 + 3.5) / 2 = 39 cm2.

Answer: Sbcmn = 39 cm2.



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