# 2021 JMPSC Accuracy Problems/Problem 3

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## Problem

In a regular octagon, the sum of any three consecutive sides is $90.$ A square is constructed using one of the sides of this octagon. What is the area of the square?

## Solution

We are given that the sum of any three sides of the octagon is 90, and since the octagon is regular, we know that all sides are equal. Thus, each side of the octagon must equal to $\frac{90}{3} = 30$. Since one side of the square shares a side with the octagon, we know the side lengths of the square are also 30. Thus, our answer is $30^2 = \boxed{900}$

## Solution 2

We have each side of the octagon is $s$, so $3s=90$, or $s=30$. This means the area of the square is $30^2=\boxed{900}$

~Geometry285