Question

What is the area of the figure?

Answer 1

Notice that the triangle is a right isosceles triangle, because the given angle measures are 45° and 90°, so the third angle measure is 180°-90°-45°=45°.

The length of the hypotenuse is 24 ft. Let the side lengths of the 2 equal sides be a.


By the Pythagorean theorem we have:


`a^2+a^2=24^2`

thus


`2a^2=24^2`

divide both sides by 2, and take the square root:


`a= (24)/( √(2) ) = (24 √(2) )/(2)=12 √(2)`


The area of the triangle is given by the formula:

(1/2)*side*side, so the area of the triangle is :


(1/2)*
`12 √(2)`*
`12 √(2)`=144 (square units)


Answer: 144 square units