The surface area of a polyhedren is the total of the area of the polygons that form its faces. For prisms, surface area is the sum of area of two bases and several parallelograms. The surface area of the prism is equal to the perimeter of the base times the sum of the apothem of the polygon and the height of the prism.

### Surface Area of a Pentagonal Prism Formula

Surface area of any prism is given by,

Surface Area of a Prism = L + 2B

Where, L is the lateral surface area and B is the base area of the prism.

Now,

**surface area of the pentagonal prism**=> S = 2(

$\frac{1}{2}$ a P) + h P

= a P + h P

= P(a + h)

=> S = P(a + h)

Where, a = apothem height of the base and h = height of the prism.

**Formula:**

Surface Area of a Pentagonal Prism = P(a + h)

Where, a = apothem height of the base and h = height of the prism.

Example:In right pentagonal prism, the apothem of the regular pentagon is 6 cm, the side of

the pentagon are 18 cm each, and the height of the prism is 14 cm. Find the surface area of the prism.

Solution:

Given:Apothem height (a) = 6 cm

Side of prism = 18 cm

Height of the prism (h) = 14 cm

Step 1:The surface area is equal to the perimeter of the base times the sum of the apothem of the polygon and the height of the prism.

Since each side of pentagonal prism is 18 cm

=> Perimeter of the base = 5 x 18 = 90 cm

Step 2:Surface Area of a Pentagonal Prism (S) = P(a + h)=> S = 90(6 + 14)

= 90 x 20

= 1800

The surface area of the pentagonal prism is 1800 cm

^{2} .