The height BH of rhombus ABCD divides its side AD into segments AH = 77 and HD = 8. Find the area of the rhombus.
| August 18, 2021 | education
Determine the length of the sides of the rhombus.
AB = BC = CD = AD = AH + DH = 77 + 8 = 85 cm.
In a right-angled triangle СDН, according to the Pythagorean theorem, we determine the length of the leg СН.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 85 ^ 2 – 77 ^ 2 = 7225 – 5929 = 1296.
BH = 36 cm.
Determine the area of the rhombus.
Savsd = AD * BH = 85 * 36 = 3060 cm2.
Answer: The area of the rhombus is 3060 cm2.
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