Answer:
144 ft²
Step-by-step explanation:
There are a number of ways you can solve this problem. One is to figure the leg lengths, and use those to compute the area of the triangle in the usual way.
AC = (24 ft)·sin(45°) = 12√2 ft
BC = (24 ft)·cos(45°) = 12√2 ft
Area = 1/2·AC·BC = (1/2)·(12√2 ft)·(12√2 ft) = 144 ft²
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Another is to recognize that the altitude from the hypotenuse of this isosceles right triangle is half the length of the hypotenuse, or 12 ft. Then the triangle area formula gives the area as ...
Area = (1/2)·AB·(AB/2) = (1/2)·(24 ft)·(12 ft) = 144 ft²
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Along the same lines, the triangle is half a square whose diagonals are both 24 ft. The area of the square is half the product of those diagonals:
square area = (1/2)·(24 ft)² = 288 ft²
The triangle area is half of that, or
Area = (1/2)(288 ft²) = 144 ft²
