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The diagram below consists of a small square, four equilateral triangles, and a large square.  Find the area of the large square.

 

 Jun 10, 2024
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Since all sides of a square are equal, the top side of the square is one. Since the sides of equilateral triangles are also the same, all of the sides on the equilateral triangles are also one. The bases of two of these equilateral triangles almost make up the side length of the large square, but there is a gap. If we continue the horizontal line made up by those two bases, we can see that the shape to the right of the last equilateral triangle is another equilateral triangle, just cut off halfway. This means that the whole length of the side of the square is 2 sides of the equilateral triangle plus one half of the side, which is 1 + 1 + 1/2 = 5/2. To find the area of the large square, we just square the side length, getting (5/2)^2 = 25/4 square units.

 Jun 10, 2024

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