The two right triangular prisms are similar. find the surface area of the larger prism. round your answer to the nearest hundredth.

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

B. 162.61 yd^2

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