Area of parallelogram ABCD = 180. E midpoint of side AB find the area of the trapezoid DAEC.
| September 3, 2021 | education
According to the formula for the area of the parallelogram S = AB * h, where h is the height drawn to the side AB.
The area of the trapezoid is equal to the half-sum of the bases of the trapezoid multiplied by the height of the trapezoid. In this case, point E is the middle of side AB. In the DAEC trapezoid, the bases are AE and DC.
DC = AB,
AE = 1/2 * AB.
The height of the DAEC trapezoid coincides with the height of the parallelogram ABCD:
S1 = 1/2 * (DC + AE) * h = 1/2 * (AB + 1/2 * AB) * h = 1.5 / 2 (AB * h).
The value of the product AB * h is equal to the area of the parallelogram, thus,
S1 = 1.5 / 2 * 180 = 135.
Answer: 135.
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