Question

A circular disc of radius 7 cm is inscribed inside an equilateral triangle. What is the approximate area of the remaining portion of the triangle?

• A. 100.66 cm²
• B. 148.2 cm²
• C. 200.3 cm²
• D. 155.6 cm²

Answer 1

Answer:

A. 100.66 cm²

A circle of radius (r = 7) cm is inscribed in an equilateral triangle.

For an equilateral triangle, the inradius is:
$r = \frac{a\sqrt{3}}{6}$

So,

$7 = \frac{a\sqrt{3}}{6}$
$\Rightarrow a = \frac{42}{\sqrt{3}} = 14\sqrt{3}$

Area of triangle

$A_{\triangle} = \frac{\sqrt{3}}{4}a^2$

$= \frac{\sqrt{3}}{4}(14\sqrt{3})^2$
$= \frac{\sqrt{3}}{4}(196 \cdot 3)$
$= \frac{588\sqrt{3}}{4}$
$= 147\sqrt{3}$

Approximate:
$147 \times 1.732 \approx 254.6\ \text{cm}^2$

Area of circle

$A_{\text{circle}} = \pi r^2 = \pi \times 49 \approx 153.94$

Remaining area

$254.6 - 153.94 \approx 100.66$