The height BH of the rhombus ABCD divides the segments AH = 44 and HD = 11. Find the area of the rhombus.
| July 3, 2021 | education
Determine the length AD of the rhombus side.
AD = AH + DH = 44 + 11 = 55 cm.
Since all sides of a rhombus are equal, then in a right-angled triangle ABN, hypotenuga AB = AD = 55 cm.
By the Pythagorean theorem, in the right-angled triangle ABN, we determine the length of the leg BN.
BH ^ 2 = AB ^ 2 – AH ^ 2 = 3025 – 1936 = 1089.
BH = 33 cm.
Determine the area of the rhombus.
Savsd = AD * BH = 55 * 33 = 1815 cm2.
Answer: The area of the rhombus is 1815 cm2.
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