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:
[tex]a^2+a^2=24^2[/tex]
thus
[tex]2a^2=24^2[/tex]
divide both sides by 2, and take the square root:
[tex]a= \frac{24}{ \sqrt{2} } = \frac{24 \sqrt{2} }{2}=12 \sqrt{2} [/tex]
The area of the triangle is given by the formula:
(1/2)*side*side, so the area of the triangle is :
(1/2)*[tex]12 \sqrt{2}[/tex]*[tex]12 \sqrt{2}[/tex]=144 (square units)
Answer: 144 square units
