The Triangles: Each triangle has an area of (1/2)*base*height. We know the side length of the triangle is 8 cm. In order to find the height of the triangle, we can use Pythagoras Theorem.

By splitting the triangle in half we have two right angled triangles made up of a hypotenuse of length 8cm and a shorter length of 4 cm. Then the remaining length is sqrt(8^2 - 4^2) = sqrt(48) = 4 * sqrt(3), which is the height.

Therefore the area of each triangle is (1/2) * base * height = 0.5 * 8 * 4 * sqrt(3) = 16 * sqrt(3) cm^2.

Since we have two triangles, the total area of the triangles is 2 * 16 * sqrt(3) = 32 * sqrt(3) cm^2.

The rectangle: By looking at the picture, we can see that the shorter length of the big rectangle in the center is 20 cm. The length of the long side is 3 * 8 = 24 cm since it is made up of three of the side lengths of the triangles. Therefore, the surface area of the rectangle is 24 * 20 = 480 cm^2.

The Entire Shape: The surface area of the entire shape is then 480 + (32 * sqrt(3)) cm^2 = 535.43 cm^2.

May 14th, 2015

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