Chapter 11, Problem 20RP

Solution

To Calculate: The area of an equilateral triangle.

The area of an equilateral triangle is $\frac{49\sqrt{3}}{4}$ unit ${}^2$

Given information:

Perimeter of an equilateral triangle is $21$

Formula used:

Here, we are using the formula:

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

(Where, “ a ” is side)

Calculation:

Perimeter = Sum of all sides

  $21=a+a+a$

  $21=3a$

  $a=7$

Now, area of an equilateral triangle = $\frac{\sqrt{3}}{4}{a}^2$

(Where, “ a ” is side)

➔$\frac{\sqrt{3}}{4}\times 7\times 7$

➔$\frac{\sqrt{3}}{4}\times 49$

➔$\frac{49\sqrt{3}}{4}$

Conclusion: Hence, the area of an equilateral triangle is $\frac{49\sqrt{3}}{4}$ unit ${}^2$