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:

$a= \frac{24}{ \sqrt{2} } = \frac{24 \sqrt{2} }{2}=12 \sqrt{2}$


The area of the triangle is given by the formula:

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


(1/2)*$12 \sqrt{2}$*$12 \sqrt{2}$=144 (square units)


Answer: 144 square units