**Finding the surface area of a prism :**

When dimensions of a prism are given, we can use the appropriate formula to find surface area of the prism.

The formula given below can be used to find surface area of a prism.

**Example 1 : **

Erin is making a jewelry box of wood in the shape of a rectangular prism. The jewelry box will have the dimensions shown below. She plans to spray paint the exterior of the box. How many square inches will she have to paint ?

**Solution : **

**Step 1 : **

Identify a base, and find its area and perimeter.

Any pair of opposite faces can be the bases. For example, we can choose the bottom and top of the box as the bases.

Find base area.

B = l x w

B = 12 x 15

B = 180 square in.

Find perimeter of the base.

P = 2(12) + 2(15)

P = 24 + 30

P = 54 in.

**Step 2 : **

Identify the height, and find the surface area.

The height h of the prism is 6 inches. Use the formula to find the surface area.

S = Ph + 2B

S = 54(6) + 2(180)

S = 684 square inches

Hence, Erin will have to spray paint 684 square inches of wood.

**Example 2 : **

A brand of uncooked spaghetti comes in a box that is a rectangular prism with a length of 9 inches, a width of 2 inches, and a height of 1 1/2 inches.What is the surface area of the box ?

**Solution : **

**Step 1 :**

Identify a base, and find its area and perimeter.

Any pair of opposite faces can be the bases. For example, we can choose the bottom and top of the box as the bases.

Find base area.

B = l x w

B = 9 x 2

B = 18 square in.

Find perimeter of the base.

P = 2(9) + 2(2)

P = 18 + 4

P = 22 in.

**Step 2 : **

Identify the height, and find the surface area.

The height h of the prism is 1 1/2 inches. Use the formula to find the surface area.

S = Ph + 2B

S = 22(1 1/2) + 2(18)

S = 22(3/2) + 36

S = 33 + 36

S = 69 square inches

Hence, the surface area of the box is 69 square inches.

After having gone through the stuff given above, we hope that the students would have understood "Finding the surface area of a prism".

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