Surface and Lateral Area of 3-D Figures - Prisms Formulas | List of Surface and Lateral Area of 3-D Figures - Prisms Formulas You Should Know - BYJUS

Surface and Lateral Area of 3-D figures - Prisms Formulas

A prism is a flat-faced polyhedron. It doesn’t have any curves. For example, a prism can be compared to a book, a cuboid-shaped aquarium, a triangular sandwich box, and so on. As a prism is made of flat polygonal surfaces, we can find its surface area. The total area occupied by the prism's faces is known as the total surface area. The shape of a 3-dimensional solid prism’s base determines its surface area. For a prism, the lateral surface area is the area of the vertical or lateral faces....Read MoreRead Less

Introduction

In geometry, surface area formulas refer to the lateral and total surface areas of various geometrical objects. Let’s have a quick recap, the surface area of an object is the total area of the object’s outside surfaces. It can also be put as the sum of the areas of all the faces of the object. It is always expressed in squared units, such as squared feet, squared yards, and so on.

The lateral surface area, on the other hand, refers to the area of the lateral surfaces. Lateral surfaces are those surfaces which are not the base and the top of the solid.

List of Formulas

The general formula is used to calculate the surface area of any prism. A prism’s total surface area is the sum of its lateral surface area and the area of its two flat bases.

Let’s calculate the surface area of the triangular prism shown below with a base ‘b’, a height ‘h’, and a length ‘L’.

There are two triangular bases on the given prism. As a result, the surface area of a prism can be calculated using the formula

$$(2 \times \text{Base Area})+(\text{Base perimeter}\times \text{length of the prism})$$

Because the base is triangular, the base area A = $$\frac{1}{2}\times b \times h$$

and, the base perimeter = The sum of the triangle’s three sides,

= (a + b + c).

Therefore, the surface area of a triangular prism = bh + (a + b + c)L or $$(2 \times A+PL)$$ is obtained by substituting the respective values in the formula.

Where, A = Base area

P = Base perimeter

L = Length of the prism

The table below shows the lateral surface area and total surface area of a prism.

Prisms come in a variety of shapes and sizes. The bases of various prisms differ, as do the formulas for calculating the prism’s surface area. To understand the implications behind the surface area of various prisms, look at the table below:

Solved Examples

Example 1: Calculate the surface area of a prism with a base area of 8 square units, a base perimeter of 12 units and a length of 4 units.

Solution:

The data provided tells us,

8 square units are used as the base area, 12 units for the base perimeter and the prism’s length is 4 units.

Surface Area of Prism = $$(2 \times \text{Base Area}~+~(\text{Base perimeter}\times\text{length})$$

As a result, the surface area of the prism will be = $$(2 \times 8~+~(12\times 4)$$

S = 64 units

Therefore, the prism has a surface area of 64 square units.

Example 2: The dimensions of a rectangular-shaped piece of land is 12 yards, 8 yards, and 18 yards. What is the box’s surface area?

Solution:

Given data,

Length of the piece of land = 12 yards.

Breadth of the piece of land = 8 yards.

Height of the piece of land = 18 yards.

As we know, the surface area of a rectangular prism = 2(lb + bh + lh)

Therefore, the surface area of the piece of land $$2(12\times 8+8\times 18+12\times 18)$$

= 2(96 + 144 + 216) (using multiplication properties)

= 2(456)

= 912 sq.yards

Example 3: Find the surface area of a room. Look at the dimensions given below.

Solution:

Given data,

Length of the box = 16 feets.

Breadth of the box = 5 feets.

Height of the box = 14 feets.

As we know, the surface area of a rectangular prism = 2(lb + bh + lh)

Therefore, the surface area of the room = $$2(16\times 5+5\times 14+16\times 14)$$

= 748sq.feets

Example 4: Find the surface area of the rectangular iron bar. Look at the dimensions given below.

Solution:

Given data,

Length of the box = 13 inches.

Breadth of the box = 6 inches.

Height of the box = 4 inches.

As we know, The surface area of a rectangular prism = 2(lb + bh + lh)

Therefore, the surface area of the rectangular iron bar = $$2(13\times 6+6\times 4+13\times 4)$$

= 308 sq.inches

The prism surface area formula is obtained by taking the sum of twice the base area and the lateral surface area of the prism. The surface area of a prism is calculated as

S = $$(2\times \text{Base Area})~+~(\text{Base perimeter}\times \text{length)})$$

where “S” denotes the prism’s surface area.

The following steps can be used to calculate the prism’s surface area:

Step 1: Look at the prism’s pattern. Make a note of the dimensions of the prism in question.

Step 2: In the surface area of the prism formula, substitute the dimensions $$(2\times \text{Base Area})~+~(\text{Base perimeter}\times \text{length)})$$.

Step 3: Determine the value of the prism’s surface area and place the unit of the prism’s surface area at the end (in terms of square units.

The surface area of a prism refers to the total area occupied by the prism. The prism’s surface area is determined by the prism’s base area as well as its lateral surface area. The area of the prism’s surface is measured in sq.m, sq.cm, sq.in, sq.ft and so on.