The two right triangular prisms are similar. Find the surface area of the larger prism. Round your answer to the nearest hundredth.
Accepted Solution
A:
You have all the dimensions of the smaller prism, so you can find its total surface area.
The smaller prism has two triangular bases with height sqrt(5) yd and base 2 yd.
Area of 1 triangular base: 1/2bh = 1/2 * 2 * sqrt(5) Area of 2 bases = 2sqrt(5) = 4.472 yd^2
The small prism has three rectangular sides. One is 5 yd by 3 yd Another one is 5 yd by 2 yd The third one is sqrt(5) yd by 5 yd
The areas of the three sides are: 5 * 3 + 5 * 2 + 5 * sqrt(5) = 36.180 yd^2
The total surface area of the small prism is 4.472 yd^2 + 36.180 yd^2 = = 40.652 yd^2
Now look at the two corresponding edges of the two prisms. The edge of the smaller prism measures 3 yd, and the corresponding edge of the large prism measures 6 yd. The lengths of the edges are in a 6/3 = 2/1 ratio. The surface areas are in a ratio that is the square of the ratio of the lengths, so the surface areas are in a (2/1)^2 = 4/1 ratio. The surface area of the large prism is 4 times larger than the surface area of the small prism.
surface area of the large prism = 4 * 40.652 yd^2 = 162.61 yd^2