The side of the rhombus is 29 and the diagonal is 42. Find the area of the rhombus
| January 30, 2021 | education
Let’s construct the ВD diagonal. The diagonals of the rhombus intersect at right angles and at the point of intersection are divided in half, then AO = AC / 2 = 42/2 = 21 cm.
Triangle AOB is rectangular, in which, according to the Pythagorean theorem, we determine the length of the leg OB.
ОВ ^ 2 = AB ^ 2 – AO ^ 2 = 841 – 441 = 400.
OB = 20 cm.
Saov = AO * ВO / 2 = 21 * 20/2 = 210 cm2.
The diagonals of the rhombus divide it into four equal triangles, then Savsd = 4 * Saov = 4 * 210 = 840 cm2.
Answer: The area of the rhombus is 840 cm2.
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