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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?

 

 Apr 19, 2021
 #1
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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

 

So

 

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

 Apr 19, 2021
 #2
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why do you have negative points?

Guest Apr 24, 2021

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