Find the side of a rhombus and its area if its diagonals are 12cm 16cm

univerkov | February 5, 2021 | education

1. The tops of the rhombus A, B, C, D. Diagonals AC = 16 cm and ВD = 12 cm. O – intersection point

diagonals. S – area.

2. Triangle ADO – rectangular. ∠AOD = 90 °, so the diagonals are perpendicular.

3.AO = 1 / 2AC = 8 cm, DO = 1/2 ВD = 6 cm (the diagonals at the intersection point are divided into

equal segments).

4. Side of the rhombus AD = √AO² + DO².

AD = √64 + 36 = 10 cm.

5. S = AC x ВD: 2 = 16 x 12: 2 = 96 cm².

Answer: the side of the rhombus is 10 cm, the area is 96 cm².

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