The height BH of parallelogram ABCD divides the ego side AD into segments AH = 1 and HD = 63
| May 8, 2021 | education
The height BH of parallelogram ABCD divides the ego side AD into segments AH = 1 and HD = 63. Parallelogram diagonal BD = 65. Find the area of the parallelogram.
The area of the parallelogram is calculated by the formula: S = a * h (a is the side of the parallelogram, h is the height drawn in it).
That is, S (ABCD) = BH * AD.
Side AD consists of two segments: AD = AH + HD = 1 + 63 = 64.
It remains to find the height of the ВН.
Consider a triangle BDH: angle H = 90 ° (since BH is height). BD = 65, DH = 63. Calculate the side of the BH by the Pythagorean theorem:
BH² = BD² – HD² = 65² – 63² = 4225 – 3969 = 256.
Hence ВН = √256 = 16.
Find the area of the parallelogram:
S (ABCD) = BH * AD = 64 * 16 = 1024 (unit ²).
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