Q. 9 - Geometry

Question

Find the area of each figure:

Step-by-Step Solution

Answer

The area of given figure is 84  square unit.

Step 1. Given information.

Step 2. Use Phythagoras theorem.

Using Pythagoras theorem finding the missing leg of the triangles first and second.

In first triangle:

$H^2=P^2+B^2$

${13}^2=5^2+B^2$

$B^2=169-25$

$B^2=144$

$B=12$

In the second triangle 

$H^2=P^2+B^2$

${15}^2=P^2+{12}^2$

$P^2=225-144$

$P^2=81$

$P=9$

Step 3. Concept used.

Area of triangle can be found using the formula 

$A=\frac{1}{2}bh$

Where, 

b= Base of a triangle and h= Height of a triangle

Step 4. Find the area of first triangle.

$A_1=\frac{1}{2}bh$

     $=\frac{1}{2}\times 12\times 5$

     $=6\times 5$

   =30   Square unit

Step 5. Find the area of second triangle.

$A_2=\frac{1}{2}bh$

     $=\frac{1}{2}\times 9\times 12$

     $=9\times 6$

    =54  Square unit

Step 6. Find the total area.

Total area of given figure

 $A=A_1+A_2$

     $=30+54$

    =84  Square unit

Therefore, the area of given figure is84 Square unit.