Q11. - Geometry

Question

Find the area of each figure:

An isosceles right triangle with hypotenuse 8

Step-by-Step Solution

Answer

The area of given figure is 16 square units.

Step 1. Analyze the given information.

Hypotenuse of triangle is given h=8

Since isosceles triangles have two sides equal.

Let the common sides be x

Then, the sides of triangle are $x,x,8$$x,x,8$

Step 2. 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.

$8^2=x^2+x^2$

$2x^2=64$

$x^2=32$

$x=4\sqrt{2}$

Then, $P=B=4\sqrt{2}$

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 given figure.

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

      $=\frac{1}{2}\times 4\sqrt{2}\times 4\sqrt{2}$

     $=2\sqrt{2}\times 4\sqrt{2}$

  =16    Square units.

Therefore, the area of given figure is16 square units.