Chapter 11.5, Problem 10PSA

To determine

To Calculate: The area of an equilateral triangle.

Answer to Problem 10PSA

The area of an equilateral triangle is $27\sqrt{3}$

Explanation of Solution

Given information:

Radius of the circle is $3$

Formula used:

Here, we are using the formula

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

Where

“ a ” is the side of the triangle.

Calculation:

Here, In the given triangle

  $\tan {30}^{\circ }=\frac{3}{x}$ ( tan $\theta =\frac{P}{B}$ )

  $\frac{1}{\sqrt{3}}=\frac{3}{x}$

  $x=3\sqrt{3}$

So, Area = $\frac{\sqrt{3}}{4}{a}^2$

  → $\frac{\sqrt{3}}{4}\times 36\times 3$

  → $27\sqrt{3}$

Conclusion: Hence,the area of an equilateral triangle is $27\sqrt{3}$