A square piece of cloth is cut from a larger square as in the figure above. The corners of the smaller square are the midpoints of the sides of the larger square. How much cloth, in square centimeters, is left over?



There are a number of ways to solve this problem. One way is to find the areas of the outside triangle pieces. Each has a base of 8 cm and a height of 8 cm.
A = \(\frac{1}{2}\)bh
A = \(\frac{1}{2}\)(8)(8)
A = 4(8)
A = 32
Since there are 4 triangles left, the total area is \(4 \times 32\), or 128, square centimeters.

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