Weird Perimeter

Geometry Level 3

In the diagram adjacent edges are at right angles. The four longer edges are equal in length, and all of the shorter edges are also equal in length. The area of the shape is 528. What is the perimeter?

Problem and Image: Courtesy Waterloo University
80 144 264 132 90

Hana Wehbi by Hana Wehbi , 51, USA

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1 solution

Hana Wehbi
Apr 3, 2017

I divided the graph into 33 33 small congruent squares. Each of the squares has an area of T o t a l A r e a 33 = 528 33 = 16 \frac{Total Area}{ 33}= \frac{528}{33}=16 .

The length of each side is 16 = 4 \sqrt{16}=4 .

By counting, we have 36 36 sides, thus the perimeter is 4 × 36 = 144 4\times 36 =144

The squares don't look congruent in scale but you've got the idea.

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