The area of the parallelogram ABCD is 132 point G midpoint of CD. Find the area of the trapezoid ABGD.
| June 26, 2021 | education
Let us drop from point G the height GH, which is both the height of the trapezoid and the height of the parallelogram.
The area of the parallelogram is Savsd = AB * GH.
The area of the trapezium АGСВ is equal to: Sagсв = (AB + GC) * GH / 2.
Since, by condition, point G is the middle of the segment DC, then GC = DC / 2 = AB / 2.
Then Sagcv = (AB + AB / 2) * GH / 2 = (3 * AB / 2) * GH / 2 = (3/4) * AB * GH.
Sagsv / Savsd = (3/4) * AB * GH / AB * GH).
Sagw = Savsd * 3/4 = 132 * 3/4 = 99 cm2.
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