Problem 5 · 2018 Math Kangaroo
Easy
Geometry & Measurement
perimeter
A star is made of a square and four triangles. All the sides of the triangles are equally long. The perimeter of the square is 36 cm. What is the perimeter of the star?
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Answer: E — 72 cm
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Hint 1 of 2
First get the side of the square from its perimeter.
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Hint 2 of 2
The star's outline is made only of the slanted triangle sides - the square's edges are hidden inside - so count how many of those equal sides form the border.
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Approach: find the equal side length, then count the edges on the star's outline
- The square has perimeter 36 cm, so each side is 9 cm.
- All the triangle sides equal that side, namely 9 cm.
- The star's boundary is the two outer sides of each of the four triangles: 4 x 2 = 8 sides.
- So the perimeter is 8 x 9 = 72 cm.
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