Q20. - Geometry

Question

Find the area of each figure:

A rectangle with length $16$ inscribed in a circle with radius $10$.

Step-by-Step Solution

Answer

The area of given figure is $192$square units.

Step 1. Analyze the given information.

Let the width of the rectangle is $a$.

Step 2. Find the width of rectangle.

We can use Pythagoras theorem.

Pythagorean Theorem define that in a right angle triangle, the square of the hypotenuse is equal to the sum of squares of other sides.

${20}^2=a^2+{16}^2$

$a^2=400-256$

$a^2=144$

$a=12$

Thus, the width of rectangle is $12$

Step 3. Find the area of rectangle.

Area of rectangle can be found using the formula 

$A=lb$

Where, 

$l=$ Length of a rectangle and $h=$ Width of a rectangle

$A=16\times 12$

      $=192$ Square units.

Therefore, the area of given figure is $192$ square units.