In a rhombus, the diagonals are 10 and 14. Find its area and perimeter.
| June 20, 2021 | education
S = ½ BD * AC = ½ * 14 * 10 = 70.
Because the diagonals of the rhombus are perpendicular and the intersection point is divided in half, then BO = ½ BD = ½ * 14 = 7.
AO = ½ AC = ½ * 10 = 5.
∠BOA = 90 °.
The ABO triangle is rectangular.
By the Pythagorean theorem, AB ^ 2 = AO ^ 2 + BO ^ 2 = 25 + 49 = 74.
AB = √74.
Perimeter P = 4AB = 4√74.
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