The height of the rhombus is 12 cm, and one of its diagonals is 15 cm. Find the area of the rhombus.

univerkov | April 12, 2021 | education

In a right-angled triangle BDH, according to the Pythagorean theorem, we determine the length of the leg DH.

DH ^ 2 = BD ^ 2 – BH ^ 2 = 15 ^ 2 – 14 ^ 2 = 225 – 144 = 81.

DН = 9 cm.

Let the length of the side of the rhombus be X cm, then AB = X cm, AH = (X – 9) cm.

In a right-angled triangle ABН, according to the Pythagorean theorem, AB ^ 2 = AH ^ 2 + BH ^ 2.

X ^ 2 = (X – 9) ^ 2 + 12 ^ 2.

X ^ 2 = X ^ 2 – 18 * X + 81 + 144.

18 * X = 225.

X = AB = AD = 12.5 cm.

Determine the area of the rhombus.

Savsd = AD * AH = 12 * 12.5 = 150 cm2.

Answer: The area of the rhombus is 150 cm2.

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