What is the perimeter of this figure? (I)

Geometry Level 2

Find the perimeter of the figure drawn in dark lines below. Assume all arcs that look like part of a circle to be part of a circle, and all angles that look perpendicular to be perpendicular.

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The answer is 40.

A Former Brilliant Member by A Former Brilliant Member

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2 solutions

Mahdi Raza
Jun 1, 2020

Watch the GIF to see how the lines can be re-arranged

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I should say that is BRILLIANT! Thanks for the solution!

A Former Brilliant Member - 1 year ago

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Thank you, glad you like it :)

Mahdi Raza - 1 year ago

Let the small horizontal segments be of lengths a , c , e , g a, c, e, g and the small vertical segments be of lengths b , d , f , h b, d, f, h respectively. Then

a + c + e + g = b + d + f + h = 10 a+c+e+g=b+d+f+h=10 .

The required perimeter is 10 + a + b + c + d + e + f + g + h + 10 = 10 + 10 + 10 + 10 = 40 10+a+b+c+d+e+f+g+h+10=10+10+10+10=\boxed {40} .

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