Question

20. What is the area of the figure. Show your work.

Answer 1

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

Answer 2

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