Answer:
336.02 square centimeters
Step-by-step explanation:
The surface area is the area of all the surfaces of the prism shown.
The prism has 7 surfaces.
Top and Bottom are pentagons with side lengths of 5.
The other 5 side surfaces are rectangles with length 10 and width 5.
Note the formulas of area of pentagon and area of rectangle below:
Area of Rectangle = Length * Width
Area of Pentagon =
, where a is the side length
Lets find area of each of the surfaces:
<u>Top Surface</u> (Pentagon with side length 5) = ![\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2=\frac{1}{4}\sqrt{25+10\sqrt{5} }* (5)^2=43.01](https://tex.z-dn.net/?f=%5Cfrac%7B1%7D%7B4%7D%5Csqrt%7B25%2B10%5Csqrt%7B5%7D%20%7D%2A%20a%5E2%3D%5Cfrac%7B1%7D%7B4%7D%5Csqrt%7B25%2B10%5Csqrt%7B5%7D%20%7D%2A%20%285%29%5E2%3D43.01)
<u>Bottom Surface</u> = same as Top Surface = 43.01
<u>Side Surface</u> (rectangle with length 10 and width 5) = 10 * 5 = 50
There are 5 side surfaces that are each 50 sq. cm. so area would be:
<u>Area of 5 Side Surface</u> = 5 * 50 = 250
Total Surface Area = 250 + 43.01 + 43.01 = 336.02 square centimeters