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 = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2[/tex] , where a is the side length
Lets find area of each of the surfaces:
Top Surface (Pentagon with side length 5) = [tex]\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2=\frac{1}{4}\sqrt{25+10\sqrt{5} }* (5)^2=43.01[/tex]
Bottom Surface = same as Top Surface = 43.01
Side Surface (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:
Area of 5 Side Surface = 5 * 50 = 250
Total Surface Area = 250 + 43.01 + 43.01 = 336.02 square centimeters
