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# Surface Area of a Prism

Prism is a three dimensional solid figure. Generally, the flat surface of the solid is known as its face. The top and bottom faces are known as bases. Faces forming the sides of the prism are also called as lateral faces or lateral surfaces. Surface area of any solid describes the material used to cover a geometrical figure and calculated in square units. Below will study about prism surface area formula and some solved examples. After this lesson you will be able to solve prism based problems at our own pace. Related Calculators Prism Surface Area Calculator Calculate Surface Area of a Rectangular Prism Surface Area of a Triangular Prism Calculator Calculate Surface Area

## Formula

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Total Surface Area is the sum of the lateral surface area and twice the base area of the prism.

Total Surface Area = $LSA + 2 \times$ Base Area

Total surface area = $(P \times h + 2 A) sq.$ units

When $P$ is the perimeter of the base, $A$ is the area of the base and h is the height of the prism.

## Lateral Surface Area

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The lateral surface area is the sum of the areas of prism's lateral faces. And it can be calculated by multiplying the perimeter of the base by the height of the prism.

Lateral Area = Perimeter of Base $\times$ Height of Prism
If $P$ is the perimeter of the base and $h$ is the height of a prism then

Lateral surface of right prism = $P\ h$

## Examples

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Given below are some of the examples:

Example 1:

Find the surface area of a prism whose base is a right angled triangle of side 8 cm, 15 cm and 17 cm, and height of the prism is 20 cm.

Solution:

The sides of the triangular base are $8 cm,\ 15 cm$ and $17 cm$ and

Height of the prism is $20 cm$

Let us take, the base of the triangle = $8 cm$

Height of the triangle = $15 cm$

The lateral surface area of the prism = $P\ h$ square units

= $(8 + 15 + 17) \times 20$

= $40 \times 20$

Lateral Surface Area = $800 sq.\ cm$

Now, the area of the bases, $A$ = $\frac{1}{2}$ $b\ h\ sq.units$

= $\frac{1}{2}$ $\times 8 \times 15$

$A$ = $60 sq.cm$

The total surface area of the prism = $P\ h\ +\ 2\ A$

= $800\ +\ 2\ \times\ 60$

Total surface area of the prism is $920\ sq.cm$

Example 2:

Find the surface area of the rectangular prism given below. Solution:

Surface area is the sum of all unit squares that fit on the exterior of a solid.

Formula for surface area of rectangular prism = $2lw + 2lh + 2wh$

where, $l$ - length, $w$ - width and $h$ - height of prism

From figure: $l$ = $10 cm,\ w$ = $4 cm$ and $h$ = $5 cm$

surface area of rectangular prism = $2 \times 10 \times 4 + 2 \times 10 \times 5 + 2 \times 4 \times 5$

= $80 + 100 + 40$

= $220$

Therefore, the surface area of rectangular prism is $220 cm^2$

 More topics in Surface Area of a Prism Lateral Surface Area of a Prism Surface Area of a Trapezoidal prism Surface Area of a Square Prism Surface Area of a Triangular Prism
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