The side of the rhombus is 4√2 and the acute angle is 45 degrees. Find the radius of the inscribed circle.
| June 20, 2021 | education
We define the area of a rhombus through the length of its side and the acute angle between them.
Savsd = AB * AD * Sin45 = 4 * √2 * 4 * √2 * √2 / 2 = 16 * √2 cm2.
Also, the area of the rhombus is equal to: Savsd = СD * НK, where НK is the height of the rhombus.
16 * √2 = 4 * √2 * NC.
НK = 16 * √2 / 4 * √2 = 4 cm.
The radius of a circle inscribed in a rhombus is half the length of its height.
R = OH = HK / 2 = 4/2 = 2 cm.
Answer: The radius of the inscribed circle is 2 cm.
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