The parallelogram heights are 4 cm and 8 cm. Perimeter = 36. Find the area.
| March 20, 2021 | education
Let side AB = DC = X cm, then, by condition, side AD = BC = Y cm.
Determine the area using the CD side and the ВC height.
S = DC * ВK = X * 8 cm2.
Determine the area using the height of the HV and the required base AD.
S = AD * BH = Y * 4 cm2.
Since the areas are the same, let’s equate their right-hand sides.
8 * X = 4 * Y.
2 * X = Y. (1).
The perimeter, by condition, is 36 cm.
2 * X + 2 * Y = 36. (2).
Let’s solve the system of equations 1 and 2.
2 * X + 2 * (2 * X) = 36.
6 * X = 36.
X = AB = DC = 36/6 = 6 cm.
Determine the area of the parallelogram.
S = DC * ВK = 6 * 8 = 48 cm2.
Answer: The area is 48 cm2.
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