SOLUTION: Mathew cuts four right angled triangles from the corners of a square cardboard. What is the perimeter of the cardboard after Mathew cuts out the triangles? the side of the squa

Algebra ->  Surface-area -> SOLUTION: Mathew cuts four right angled triangles from the corners of a square cardboard. What is the perimeter of the cardboard after Mathew cuts out the triangles? the side of the squa      Log On


   

Question 959232: Mathew cuts four right angled triangles from the corners of a square cardboard. What is the perimeter of the cardboard after Mathew cuts out the triangles?
the side of the square is 8 units, and the right triangles on the corners are 2 units per leg.
Answer by macston(5194) About Me  (Show Source):
You can put this solution on YOUR website!
The uncut portion of the square=8in-2(2in)=8in-4in=4inches
The length of diagonals is hypotenuse of right triangle with legs=2 inches:
The four diagonal cuts=sqrt%282%5E2%2B2%5E2%29=sqrt%282%2A4%29=2sqrt%282%29
There are four slanted corners and four uncut portions so:
Perimeter=4%282sqrt%282%29in%29%2B4%284in%29=8sqrt%282%29in%2B16in=11.3in%2B16in=27.3in
ANSWER: The perimeter of the irregular octagon is 27.3 inches.