Geometry

Geometry Level 4

A circle is inscribed in a rhombus of diagonals measuring 12 cm and 24 cm. Find the area of the inscribed circle.


The answer is 90.48.

Bulbuul Dev by Bulbuul Dev , 37, India

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1 solution

Consider the quarter rhombus a right triangle with legs 24 2 = 12 a n d 12 2 = 6 \dfrac{24} 2=12 \ and\ \dfrac{12} 2=6 . The altitude from 90 degree vertex is the inradius. The hypotenuse of this big triangle is 1 2 2 + 6 2 = 6 5 . \sqrt{12^2+6^2}=6\sqrt5. From big and small similar triangle, 6 : 6 5 : : r : 12. r = 12 5 . ∴ a r e a = 144 5 ∗ π = 90.477 6:6\sqrt5::r:12. \ \ r=\dfrac {12}{\sqrt5}.\ \ \therefore\ area=\dfrac{144} 5*\pi=90.477 .

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