Chapter 11.5, Problem 2PSA

a

To determine

To calculate : The area of the equilateral triangle with side length $6$

Answer to Problem 2PSA

The area is $A=9\sqrt{3}{\text{ units}}^2$

Explanation of Solution

Given information : The side of the equilateral triangle is, $a=6$

Formula used : The area of an equilateral triangle

  $A=\frac{\sqrt{3}}{4}{a}^2$

Calculation : Substituting the value of $a=6$ in the equation, we get

  $\begin{array}{l}$ A=\frac{\sqrt{3}}{4}{(6)}^2$A=9\sqrt{3}{\text{ units}}^2\end{array}$

Thus, we get

  $A=9\sqrt{3}{\text{ units}}^2$

b

To determine

To calculate : The area of the equilateral triangle with side length $7$

Answer to Problem 2PSA

The area is $A=\frac{49\sqrt{3}}{4}{\text{ units}}^2$

Explanation of Solution

Given information : The side of the equilateral triangle is, $a=7$

Formula used : The area of an equilateral triangle is given as

  $A=\frac{\sqrt{3}}{4}{a}^2$

Calculation : Substituting the value of $a=7$ in the equation, we get

  $\begin{array}{l}$ A=\frac{\sqrt{3}}{4}{(7)}^2$A=\frac{49\sqrt{3}}{4}{\text{ units}}^2\end{array}$

Thus, we get

  $A=\frac{49\sqrt{3}}{4}$

c

To determine

To calculate : The area of the equilateral triangle with side length $8$

Answer to Problem 2PSA

The area is $A=16\sqrt{3}$

Explanation of Solution

Given information : The side of the equilateral triangle is, $a=8$

Formula used : The area of an equilateral triangle

  $A=\frac{\sqrt{3}}{4}{a}^2$

Calculation : Substituting the value of $a=8$ in the equation, we get

  $\begin{array}{l}$ A=\frac{\sqrt{3}}{4}{(8)}^2$A=16\sqrt{3}\end{array}$

Thus, we get

  $A=16\sqrt{3}{\text{ units}}^2$

d

To determine

To calculate : The area of the equilateral triangle with side length $2\sqrt{3}$

Answer to Problem 2PSA

The area is $A=3\sqrt{3}$

Explanation of Solution

Given information : The side of the equilateral triangle is, $a=2\sqrt{3}$

Formula used : We use the following formula to find the area of an equilateral triangle

  $A=\frac{\sqrt{3}}{4}{a}^2$

Calculation : Substituting the value of $a=2\sqrt{3}$ in the equation, we get

  $\begin{array}{l}$ A=\frac{\sqrt{3}}{4}{(2\sqrt{3})}^2$A=3\sqrt{3}\end{array}$

Thus, we get

  $A=3\sqrt{3}$