Question

Can anyone help me? I've been stuck with this problem for hours

Answer 1

336.02 square centimeters

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 =
`(1)/(4)\sqrt{25+10√(5) }* a^2` , where a is the side length

Lets find area of each of the surfaces:

Top Surface (Pentagon with side length 5) =
`(1)/(4)\sqrt{25+10√(5) }* a^2=(1)/(4)\sqrt{25+10√(5) }* (5)^2=43.01`

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