In trapezoid ABCD, it is known that AD = 5, BC = 1, and its area is 12.

| April 12, 2021 | education

In trapezoid ABCD, it is known that AD = 5, BC = 1, and its area is 12. Find the area of trapezoid BCNM, where MN is the middle line of trapezoid ABCD.

Let us draw the height of the CH of the trapezoid from the top of the obtuse angle, and from the formula for the area of the trapezoid we express the length of the height of the CH.

S = (BC + AD) * CH / 2.

CH = 2 * S / (BC + AD).

CH = 2 * 12 / (1 + 5) = 4 cm.

By the property of the middle line of the trapezoid, it divides the height of the CH into two equal segments. СK = NK = CH / 2 = 4/2 = 2 cm.

Determine the length of the midline MN.

MN = (BP + BC) / 2 = (5 + 1) / 2 = 3 cm.

Let us determine the area of the trapezoid BCNM.

Sdcnm = (BC + MN) * СK / 2 = (1 + 3) * 2/2 = 4 cm2.

Answer: The area of the trapezium BCNM is 4 cm2.

 



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