The area of the parallelogram ABCD is 126. Point E is the midpoint of side AB. Find the area of the trapezoid.
| February 23, 2021 | education
From point E we drop the perpendicular to the side CD. It will be the height for both the parallelogram and trapezoid EBCD. Let’s denote the height by h.
Let’s denote the base of CD by b.
The area of the parallelogram is equal to the product of the base and the height.
Sп = b * h = 126.
The area of the trapezoid is equal to the product of the half-sum of the bases and the height:
Str = (b + 0.5 * b) / 2 * h = 1.5 * b / 2 * h = 0.75 * (b * h) = 0.75 * 126 = 94.5.
Answer: the area of the trapezoid is 94.5.
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