# Geometry problems with area and volume

1. Find the area of the triangle.

2. There is a shaded triangular prism 6in x 8in x 11in with a rectangle solid 3in x 4in x 11in not shaded. Find the volume of the shaded area.

3. Given the graph, name an edge that is a bridge, if any.

4. Find the area in meters of a trapezoid with a height of 4 m and bases of 8 m and 17 m.

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## SOLUTION This solution is **FREE** courtesy of BrainMass!

1.

Keep in mind that the height of the triangle is in yards. You need to change that to feet before finding the area.

The area of a triangle can be found by multiplying the base and the height of the triangle and dividing it by two. Whereas the two measurements shown are 6 feet and 2 feet, multiplying them gives 12 and dividing by two gives 6. So, the answer is 6 ft2.

If the height was 6 yards instead of feet, then we would need to convert that into feet first. Since there are 3 feet in one yard, there are 3 * 6 = 18 feet in 6 yards. So we would then find the area of the triangle by multiplying 2 and 18 to get 2 * 18 = 36 and then you would divide by two to get an area of 18 ft2.

2.

Assuming that the triangle base of the triangular prism is a right triangle, then the volume of the triangular prism is found by finding the area of the base which would be half of the 6 in. base which is 3 in. times the height of the triangle times the length of the prism. So we get a volume of 3 * 8 * 11 = 264 in3. Finding the volume of the rectangle prism is simply the length times the width times the height so we get 3 * 4 * 11 = 132 in3. If the rectangular prism is inside the triangular prism, then we just subtract the two to find the volume of the shaded region which is 264 - 132 = 132 in3.

3.

The only bridge is the edge DE since its removal from the graph means that there will be two separate components or parts of the graph left over. Removing any other edge will still leave paths to all of the vertices.

4.

The area of a trapezoid is half of the height times the sum of the bases. Half of the height is 2 m and the sum of the bases is 8 m + 17 m = 25 m. Multiplying these together gives 2 * 25 = 50 m2

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