Calculate the area of the parallelogram ABCD if AB = BD = 20cm, AD = 16cm.
| May 31, 2021 | education
Since, by condition, AB = BD, then triangle ABD is isosceles, AB = BD = 20 cm.
Let’s draw the height BH, which is also the median of the triangle ABD, then AH = DH = AD / 2 = 16/2 = 8 cm.
From the right-angled triangle ABH, we determine the length of the BH leg.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 20 ^ 2 – 8 ^ 2 = 400 – 64 = 336.
BH = 4 * √21 cm.
Determine the area of the parallelogram.
Savsd = АD * BН = 16 * 4 * √21 = 64 * √21 cm2.
Answer: The area of the parallelogram is 64 * √21 cm2.
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