A square has a side length of 10 inches. Congruent isosceles right triangles are cut off each corner so that the resulting octagon has side lengths of 4 and 3*sqrt(2). What is the area of the octagon?
Let the side length of the octagon = S.....this = the hypotenuse of an isosceles triangle
So...the length of one of the legs of the isosceles triangles = S/√2
And the side of the square =
S + 2S/√2 = S + S√2
S + S√2 = 10
S(1 + √2) = 10 divide bot sides by ( 1 + √2)
S = 10 / ( 1 + √2 ) ≈ 4.14 (inches)"
WORDS FROM CPhill
Hope it helps~TinderWolf