How to find area

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ISEE Upper Level Quantitative Reasoning › How to find area

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Rectangle 1

The above rectangle, which has perimeter 360, is divided into squares of equal size. Give the area of the shaded portion.

Explanation

The sides of the rectangle, in total, are divided into 18 segments of equal measure, as indicated below:

Rectangle 2

The rectangle has a total perimeter of 360, so each segment - one side of a square - measures $36 0 \div 18 = 20$ . Each square has area $20 ^{2} = 400$ , so the shaded portion of the rectangle, which comprises seven squares, has area

$400 \times 7 = 2,800$ .

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