# 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)

- 98.688 sq cm
- 100 sq cm
- 101 sq cm
- 95 sq cm

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**Answer: (1) 98.688 cm ^{2}**

**Explanation:-**

**Formula-**

**The area of the equilateral triangle = sqrt.3 x a ^{2}/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 cm

^{2}

In triangle OLQ,

tan 30

^{o}= 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 r**

^{2}= 3.14 x (4 sqrt.3)

^{2}

= 3.14 x 16 x 3

= 150.72 cm

^{2}

The area of the remaining part = The area of the equilateral triangle PQR – The area of the circle

= 249.408 – 150.72

= 98.688 cm

^{2}

Hence, the answer is (1) 98.688 cm^{2.}