# What is the Remaining Portion of the Area? If

In an equilateral triangle of side 24 m, a circle is inscribed touching its sides. The area of the remaining portion of the triangle is ( √3 = 1.732)

1. 98.688 sq cm
2. 100 sq cm
3. 101 sq cm
4. 95 sq cm
Manish Listener Asked on 17th July 2015 in

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Explanation:-
Formula-
The area of the equilateral triangle = sqrt.3 x a2/4
Given-
In the figure –

Side of equilateral triangle = 24 cm
Then, the area of the equilateral triangle = sqrt.3 x 24 x 24/4
= 1.732 x 6 x 24                       (sqrt.3 = 1.732)
= 249.408 cm2
In triangle OLQ,
tan 30o = OL/LQ
1/sqrt.3 = r/12
r = 12/sqrt.3
r = 12 sqrt.3/3
r = 4 sqrt.3
Formula-
The area of the circle = pie x r2
= 3.14 x (4 sqrt.3)2
= 3.14 x 16 x 3
= 150.72 cm2
The area of the remaining part = The area of the equilateral triangle PQR – The area of the circle
= 249.408 – 150.72
= 98.688 cm2

Hence, the answer is (1) 98.688 cm2.

Anurag Mishra Professor Answered on 17th July 2015.