Chapter 8.3, Problem 54STP

To determine

The area of the square ABCD.

Answer to Problem 54STP

  $64\text{square units}$

Explanation of Solution

Given:

The given figure is:

Calculation:

According to Sine rule:

  $\begin{array}{l}\frac{AD}{\sin 90°}=\frac{4\sqrt{3}}{\sin 60°}\\ AD=4\sqrt{3}\left(\frac{2}{\sqrt{3}}\right)\\ AD=8\end{array}$

The area of the square ABCD will be:

  $\begin{array}{l}=x^2\\ ={\left(8\right)}^2\\ =64\text{square units}\end{array}$