Q10. - Geometry

Question

Find the area of each figure:

An isosceles triangle with base  10 and Perimeter 36 .

Step-by-Step Solution

Answer

The area of given figure is 60 square units.

Step 1. Given information.

Base $b=10$  and Perimeter is  36.

Step 2. Analyze the given information.

If $b=10$  and Perimeter is 36 , 

Then, the sum of other two sides of triangle  $=36-10=26$

Since isosceles triangles have two sides equal.

So, we get equal sides $=\frac{26}{2}=13$

Step 3. Find the height of triangle.

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.

 ${13}^2=5^2+P^2$

 $P^2=169-25$

 $P^2=144$

 $P=12$

Step 4. Find the area of given figure.

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

$A=\frac{1}{2}\times 10\times 12$ 

      $=5\times 12$   

    =60    Square units.

Therefore, the area of given figure is 60 square units.