Question

Q8. A circle is inscribed in an equilateral triangle of side 2424 cm, touching its sides. What is the area of
the remaining portion of the triangle?

Answer 1

Answer:

Remaining area = 98.56cm^2

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Step-by-step explanation:

Answer 2

The area of the remaining portion of the triangle is 98.6 cm^2.

Given:

A circle is inscribed in an equilateral triangle of side 24 cm, touching its sides.

To Find:

The area of the remaining portion of the triangle

Solution:

a = 24 cm

Area of equilateral triangle = $\frac{\sqrt{3} a^2 }{4}$

= $\frac{\sqrt{3} *24^2 }{4}$

=$144\sqrt{3} cm^2$

= $144 * 1.73 = 249.4 cm^2$ --- eq1

Radius of inscribed circle = $\frac{a}{2\sqrt{3} }$

r = $\frac{24}{2\sqrt{3} }$

r = $\frac{12}{\sqrt{3} }$ = $4\sqrt{3} cm$

Area of the inscribed circle = πr²

= $\frac{22}{7} * (4\sqrt{3})^2$

= $150.8 cm^2$ ---- eq2

The area of the remaining portion of the triangle eq1 - eq2

= 249.4 - 150.8

= 98.6 cm^2

Therefore, the area of the remaining portion of the triangle is 98.6 cm^2.

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