In the trapezoid ABCD AD = 5, BC = 2, and the area is also 28. Find the area of the trapezoid BCNM

| April 4, 2021 | education

In the trapezoid ABCD AD = 5, BC = 2, and the area is also 28. Find the area of the trapezoid BCNM, where NM is the middle line of the trapezoid ABCD.

Knowing the lengths of the bases of the trapezoid, we determine its midline.

MN = (AD + BC) / 2 = (5 + 2) / 2 = 3.5 cm.

From the top of the trapezoid, we draw the height of the ВН.

Determine the length of the height of the trapezoid through its area and midline.

S = BH * MN.

28 = BH * 3.5.

BH = 28 / 3.5 = 8 cm.

Consider a right-angled triangle ABН, in which point M of side AB is its midpoint, AM = BM, and the segment MK is parallel to AH, then MK is the middle line of triangle ABН, which means ВK = KN = ВН / 2 = 8/2 = 4 cm.

The VK segment is the height of the MBCN trapezoid, then the area of ​​the MBCN trapezoid will be equal to:

Smvcn = (BC + MN) * ВK / 2 = (2 + 3.5) * 4/2 = 11 cm2.

Answer: Smvcn = 11 cm2.



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