The perimeter of the rhombus is 52 cm, and one of its diagonals is 10 cm, find the area of the rhombus.
| March 26, 2021 | education
Find the side of the rhombus. Divide the perimeter by 4.
a = 52 cm ÷ 4 = 13 cm.
Find half of the known diagonal.
d1 = 10 cm ÷ 2 = 5 cm.
Find half of the second diagonal by the Pythagorean theorem.
d2 = √ (169 cm² – 25 cm²) = √144 cm² = 12 cm.
Find the entire length of the second diagonal.
D2 = 12 cm * 2 = 24 cm.
Find the area of the rhombus.
S = 10 cm * 24 cm ÷ 2 = 120 cm².
Answer: the area of the rhombus is 120 cm².
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