Question

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

Answer 1

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 = $\frac{1}{4}\sqrt{25+10\sqrt{5} }* a^2$ ,  where a is the side length

Lets find area of each of the surfaces:

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

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