Q.47 - Precalculus Enhanced with Graphing Utilities

Question

Find the area of the square in the figure.

Step-by-Step Solution

Answer

The area of the square in the given figure is 18

Step. 1 Given statement

Here square inscribed in a circle , the equation  is given.

We have to find out the area of a squre

Step 2. Finding the radius and diameter

According to the figure equation of a circle $x^2+y^2=9$ is given. This equation  is the in the  form of standard equation of a circle at origin (0,0) and radius r ,$x^2+y^2 =r^2$

 Thus  here radius r=3 and diameter is 6 , since the diameter is 2times of radius

Step.3 Finding area of the square

In this question square is inscribed in a circle and the radius of this circle is 3 , thus  diameter is 6.

 we can see in the given figure diameter  of the circle is the diagonal of a square. So area  of a square is $$\begin{gathered} A =\frac{d^2}{2} ,d= diagonal \\ =\frac{6^2}{2} \\ =\frac{36}{2} \\ =18 \end{gathered}$$