Calculate the Perimeter

Geometry Level 1

Here is a rectangle The 8-sided shape is made from these rectangles and 4 congruent right-angled triangles.

What is the perimeter of the 8-sided shape?


The answer is 48.

Jonathan Wainwright by Jonathan Wainwright , 24, United Kingdom

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2 solutions

Chew-Seong Cheong
May 22, 2019

We note that the octagon is made of four 2 × 8 2 \times 8 rectangles and four right triangles with legs 6 and 8. By Pythagorean theorem, the long sides or the octagon or the hypotenuse of the right triangle is 6 2 + 8 2 = 10 \sqrt {6^2+8^2} = 10 . Therefore, the perimeter of the octagon is 4 ( 2 + 10 ) = 48 4 (2+10) = \boxed{48} .

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Perimeter of the figure is 4[2+√{ 8 2 8^2 + ( 8 − 2 ) 2 (8-2)^2 }]=48

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