20. What is the area of the figure. Show your work.
2 answers:
Since this is an isosceles right triangle, the legs are of equal length. By the Pythagorean Theorem: 24^2=s^2+s^2 24^2=2s^2 2s^2=576 s^2=288 The area of a triangle is A=bh/2, in this case b=h=s so the area of the triangle is: A=s^2/2, and we saw earlier that s^2=288 so A=288/2 A=144 ft^2
The ratio of the 2 legs and hypotenuse in this triangle is 1:1:sqrt2 so by proportion length of one leg is 24 / sqrt2 = 16.971 Area of the triangle = 1/2 * 16.971 * 16.971 = 144 sq ft
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