The height BH of rhombus ABCD divides its side AD into segments AH = 11 and HD = 50. Find the area of the rhombus.
| September 5, 2021 | education
Determine the length of the side of the rhombus: AD = AH + DH = 11 + 50 = 61 cm.
Since all sides of a rhombus are equal, then AB = BC = CD = AD = 61 cm.
In a right-angled triangle ABH, according to the Pythagorean theorem, we determine the length of the leg BH.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 612 – 112 = 3721 – 121 – 3600.
BH = 60 cm.
Determine the area of the rhombus.
Savsd = AD * BH = 61 * 60 = 3660 cm2.
Answer: The area of the rhombus is 3660 cm2.
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