In parallelogram ABCD AB = BD, AD = 12, sinA = 0.8. Find the area of the parallelogram.
| June 25, 2021 | education
Since AB = BD, triangle ABD is isosceles. We will construct the height BH, which is also the median of the triangle ABD, then AH = DH = AD / 2 = 12/2 = 6 cm.
Cos2A = 1 – Sin2A = 1 – 0.64 = 0.36.
CosA = 0.6 = AH / AB.
AB = AH / 0.6 = 6 / 0.6 = 10 cm, then the parallelogram area is:
Savsd = AB * AD * SinA = 10 * 12 * 0.8 = 96 cm2.
Answer: The area of the parallelogram is 96 cm2.
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