Question

Find the area of each figure:

An isosceles triangle with base10and Perimeter 36 .

Short answer

The area of given figure is 60 square units.

Step-by-step solution

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 atriangleand h= Height of atriangle

$A=\frac{1}{2}\times 10\times 12$

$=5\times 12$

=60 Square units.

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