In trapezoid ABCD, the bases of AD and BC are 7 and 1, respectively, and its area is 64. Find the area of the trapezoid BCNM

| January 4, 2021 | education

In trapezoid ABCD, the bases of AD and BC are 7 and 1, respectively, and its area is 64. Find the area of the trapezoid BCNM, where MN is the middle line of the trapezoid ABCD.

Let us express the height h through the formula for the area of the trapezoid:
S = (a + b) / 2 * h →
h = (2S) / (a + b) = (2 * 64) / (7 + 1) = 128/8 = 16.
Since the middle line of the trapezoid ABCD divides its height in half, the height of the trapezoid DCNM is:
h = 16/2 = 8.
The midline of the larger trapezoid will serve as the larger base of the smaller trapezoid. Therefore, the middle line m is equal to:
m = (a + b) / 2 = (7 + 1) / 2 = 8/2 = 4.
Therefore, we calculate the area of the trapezoid:
S = (m + b) / 2 * h = (4 + 1) / 2 * 8 = 5/2 * 8 = 5/1 * 4 = 5 * 4 = 20.
Answer: 20.



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