Q9. - Geometry

Question

Find the area of each figure:

Step-by-Step Solution

Answer

The area of given figure is 30 square units.

Step 1. Given information.

The sides of triangle are $5,12$  and 13 .

i.e. $a=5,b=12$ and  

Step 2. Concept used.

Area of triangle can be found using the Heron’s formula 

$A=\sqrt{s(s-a)(s-b)(s-c)}$ 

Where, 

Semi perimeter $s=\frac{1}{2}(a+b+c)$  

Step 3. Find the semi perimeter.

$s=\frac{1}{2}(a+b+c)$

$=\frac{1}{2}(5+12+13)$

$=\frac{1}{2}\left(30\right)$

$=15$

Step 4. Find the area of given figure.

Calculation:$A=\sqrt{s(s-a)(s-b)(s-c)}$

 $=\sqrt{15(15-5)(15-12)(15-13)}$

      $=\sqrt{15\left(10\right)\left(3\right)\left(3\right)}$

       $=\sqrt{100}$

         

     $=30$  Square units.

Therefore, the area of given figure is 30  square units.