In the figure above, CDE is an equilateral triangle and ABCE is a square with an area of 1. What is the perimeter of polygon ABCDE?
4
5
6
7
8
A
5
B
6
C
4
D
7
E
8
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Solution
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As △CDE is equilateral,
let CD=DE=EC=x
As ABCE is a square and CE=x,
⇒EC=BC=BA=AE=x
Given, Area of the square ABCE=1
⇒x2=1
⇒x=1
Perimeter of the polygon ABCDE=AB+BC+CD+DE+EA
=x+x+x+x+x
=5x
=5×x
=5×1
=5
Therefore, perimeter of the polygon ABCDE is ′5′.
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