In trapezoid ABCD, the bases of AD and BC are 4 and 3, respectively, and its area is equal to 84.

| May 28, 2021 | education

In trapezoid ABCD, the bases of AD and BC are 4 and 3, respectively, and its area is equal to 84. Find the area of the trapezoid BCNM, where MN is the midline of trapezoid ABCD.

The area of the trapezoid is equal to the product of the midline of the trapezoid by the height of the trapezoid:

S = m * H.

The midline of the trapezoid ABCD is equal to the half-sum of the base of the trapezoid:

m = MN = (BC + AD) / 2 = (3 + 4) / 2 = 3.5.

Therefore, the height of the trapezoid ABCD is H = S / m = 84 / 3.5 = 24.

Since the middle line divides the height of the trapezoid into two equal segments, therefore, the height of the BCNM trapezoid is h = 24/2 = 12.

Then, the area of the trapezoid BCNM is equal to:

S = ((BC + MN) / 2) * h = ((3 + 3.5) / 2) * 12 = 3.25 * 12 = 39.

Answer: The area of the trapezoid BCNM is 39.



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