An umbrella is made by stitching 10 triangular pieces, of cloth of two different colors, each piece measuring 20 cm long, 50 cm and 50 cm. How much cloth of each color is required for the umbrella?

## An umbrella is made by stitching 10 triangular pieces, of cloth of two different colors, each piece measuring 20 cm long, 50 cm and 50 cm.

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# 1 Answer

These triangular pieces are all isosceles triangles. Therefore the altitude that connects to the base of the triangle for each piece would also bisect the base. It would cut the base into two 10 cm sides. To find the length of altitude, we do Pythagorean
theorem:

10^2 + b^2 = 50^2

b^2 = 2400

b = (2400)^.5 = 20(6)^.5

Now we can find the area of the triangular piece:

Area = .5 * base * height = .5(20)(20)(6)^.5 = 200(6)^.5

One color in this case has 5 triangular pieces

5 * 200(6)^.5 = 1000(6)^.5 = 2449.5 cm^2