Surface Area of Prism- Formula, Definition, Solved Examples (2024)

The surface area of a 3-dimensional solid prism depends upon the shape of its base. The surface area of a prism is the total area occupied by the faces of the prism. A prism is a polyhedron with flat faces. It has no curves.

1.What is the Surface Area of Prism?
2.How to Calculate the Surface Area of Prism?
3.FAQs on Surface Area of a Rectangular Prism

What is the Surface Area of Prism?

The surface area of a prism refers to the amount of total space occupied by the flat faces of the prism. Finding the surface area of a prism means calculating the total space occupied by all the faces of that respective type of prism or the sum of the areas of all faces (or surfaces) in a 3D plane.

Surface Area of a Prism Formula

To find the surface area of any kind of prism we use the general formula. The total surface area of a prism is the sum of lateral surface area and area of two flat bases. Let us look at the surface area of the prism formula

The lateral area is the area of the vertical faces, in case a prism has its bases facing up and down. Thus, the lateral surface area of prism = base perimeter × height
The total surface area of a Prism = Lateral surface area of prism + area of the two bases = (2 × Base Area) + Lateral surface area or (2 × Base Area) + (Base perimeter × height).

There are various types of prisms. The bases of different types of prisms are different so are the formulas to determine the surface area of the prism. See the table below to understand this concept behind the surface area of various prism:

ShapeBaseSurface Area of Prism = (2 × Base Area) + (Base perimeter × height)
Triangular PrismTriangularSurface area of triangular prism = bh + (s1 + s2 + b)H
Square PrismSquareSurface area of square prism = 2a2 + 4ah
Rectangular PrismRectangularSurface area of rectangular prism = 2(lb + bh + lh)
Trapezoidal PrismTrapezoidalSurface area of trapezoidal prism = h (b + d) + l (a + b + c + d)
Pentagonal PrismPentagonalSurface area of pentagonal prism = 5ab + 5bh
Hexagonal PrismHexagonalSurface area of hexagonal prism = 6b(a + h)
Surface area of regular hexagonal prism = 6ah + 3√3a2
Octagonal PrismOctagonalSurface area of octagonal prism = 4a2 (1 + √2) + 8aH

Check out types of prisms to get more details about various prisms.

Let us calculate the surface area of the triangular prism given below with a base "b", the height of prism "h", and length "L".

Surface Area of Prism- Formula, Definition, Solved Examples (1)

The given prism has two triangular bases. Therefore, according to the surface area of the prism formula (2 × Base Area) + (Base perimeter × height). Here the base is triangular so the base area A = ½ bh, and the base perimeter = the sum of three sides of the triangle let's say (a + b + c). On substituting the respective values in the formula we have, the surface area of a triangular prism = bh + (a + b + c)H = .(2A + PH)

How to Calculate the Surface Area of Prism?

The steps to determine the surface area of the prism are:

  • Step 1: Note down the given dimensions of the prism.
  • Step 2: Substitute the dimensions in the surface area of prism formula (2 × Base Area) + (Base perimeter × height).
  • Step 3: The value of the surface area of the prism is obtained and the unit of the surface area of the prism is placed in the end (in terms of square units).

Example: Find the surface area of a prism given above whose base area is 12 square units, the base perimeter is 18 units and the height of the prism is 6 units.

Solution: As we know, the surface area of the prism is given as
Surface Area of Prism = (2 × Base Area) + (Base perimeter × height)
Base area = 12 square units
Base perimeter = 18 units
Height of the prism = 6 units
Thus, Surface Area of Prism = (2 × 12) + (18 × 6)
⇒ S = 132 units2
∴ The surface area of prism is 132 square units.

Related Topics

Listed below are a few interesting topics that are related to the surface area of a prism.

  • Pyramids
  • Surface Area of Pyramid
  • Surface Area of Prism Calculator

FAQs on Surface Area of Prism

What is the Definition of the Surface Area of Prism?

The amount of area occupied by a prism is referred to as the surface area of a prism. The surface area of the prism depends on the base area of the prism and the lateral surface area of the prism. The unit of the surface area of the prism is expressed in m2, cm2, in2, or ft2.

What is the Formula for Surface Area of Prism?

The formula for the surface area of a prism 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 given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.

How to Find the Surface Area of Prism?

We can find the surface area of the prism using the following steps:

  • Step 1: Observe the pattern of the prism. Write down the given dimensions of the respective prism.
  • Step 2: Substitute the dimensions in the surface area of prism formula (2 × Base Area) + (Base perimeter × height).
  • Step 3: The value of the surface area of the prism is obtained and the unit of the surface area of the prism is placed in the end (in terms of square units).

How Do You Find the Base Area of Prism If the Surface Area of Prism is Given?

The steps to determine the base area of the prism, if the surface area of the prism is given, is:

  • Step 1: Write the given dimensions of the prism.
  • Step 2: Substitute the given values in the formula S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.
  • Step 3: Now solve the equation for "Base Area by simplifying the equations".
  • Step 4: Once the value of the base area of the prism is obtained, write the unit of the base area prism in terms of square units.

What Happens to the Surface Area of Prism If the Base Area of Prism is Doubled?

The surface area of a prism depends on the base area of the prism and the lateral surface area of the prism. Let us substitute the value of the base area as 2B in the surface area of the prism formula. The final result we have, B' = 2B, thus S' = (4 × Base Area) + (Base perimeter × height).Thus, only the final value of the surface area of the prism will increase if the base area of the prism is doubled but the value of surface area will definitely not get doubled or quadrupled.

What Happens to the Surface Area of Prism When the Height of Prism is Doubled?

The surface area of the prism depends on the base area of the prism and the lateral surface area of the prism. This lateral surface area has an important parameter that is the height of the prism. Let us substitute the value of the height of prism as 2H in the surface area of the prism formula. The final result we have, H' = 2H, thus S' = (2 × Base Area) + (Base perimeter × 2H). Thus, only the final value of the surface area of the prism will increase if the height of the prism is doubled but the value of surface area will definitely not get doubled or quadrupled.

How Does the Surface Area of Prism Change If the Type of Prism Changes?

The surface area of the prism depends on the base area of the prism and the lateral surface area of the prism. Different types of prisms have different bases hence, as the type of prism changes, the base of the prism changes. This changes the base area of the prism changes which in turn changes the surface area of the prism.

Surface Area of Prism- Formula, Definition, Solved Examples (2024)

FAQs

Surface Area of Prism- Formula, Definition, Solved Examples? ›

A right prism is made up of two identical, parallel bases on the ends, and the faces are perpendicular to the bases. The formula for finding surface area is 2B + hP (where B is the area of one of the bases, h is the prism's height and P is the perimeter of the base).

What is the formula for surface area of a prism example? ›

To find the surface area of a prism, use the formula SA=2B+ph, where SA stands for surface area, B stands for the area of the base of the prism, p stands for the perimeter of the base, and h stands for height of the prism. Since this is a rectangular prism, substitute the area formula of a rectangle for B.

What is surface area of prism grade 6? ›

The surface area of a prism is the sum of the areas of all its faces. A two-dimensional representation of a solid is called a net.

What is the formula for a prism example? ›

Prism volume (V) = B × h, where, B is the area of the base and h is the height of the prism. = l × w × h, where l, w, and h are the length, width, and height of the rectangular prism. Here, the length of the prism can be taken as the height of the prism.

What is the TSA formula for a prism? ›

We know that the general formula for the total surface area of a right prism is T. S. A. = PH+2A, where P is the base perimeter, A is the base area, and H is the height of the prism.

How to solve surface area? ›

Surface area is total area on the surface of a three-dimensional shape. To find the surface area of a cuboid which has 6 rectangular faces, add the areas of all 6 faces. Or, you can label the length (l), width (w), and height (h) of the cuboid and use the formula: surface area (SA)=2lw+2lh+2hw.

What is an example of a surface area in math? ›

Surface area is a two-dimensional measure, while volume is a three-dimensional measure. Two figures can have the same volume but different surface areas. For example: A rectangular prism with side lengths of 1 cm, 2 cm, and 2 cm has a volume of 4 cu cm and a surface area of 16 sq cm.

What is the total surface area of the prism calculator? ›

If “l” is the length, and “h” is the height and “w” is the width of the rectangular prism, the surface area is given by the formula, The surface area of a rectangular prism = 2 (lw+lh+hw) square units.

What are 3 examples of a prism? ›

Notebooks, ice cubes, and dice are a few everyday examples of prisms.

What is the prism answer? ›

Prism is a three-dimensional solid object in which the two ends are identical. It is the combination of the flat faces, identical bases and equal cross-sections.

What is the surface area and volume of a prism? ›

What is important to note is that the surface area of a right prism is the sum of the lateral area, sometimes called the net, and twice the area of a base. And to find the volume of a right prism, we simply find the product of the area of the base and the height of the prism.

How to calculate surface area of prism? ›

The formula for the surface area of a prism 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 given as S = (2 × Base Area) + (Base perimeter × height) where "S" is the surface area of the prism.

Which is a correct method for finding the surface area of prisms? ›

To calculate the total surface area of a prism:
  • Find the area of the two end faces.
  • Work out the area of all the rectangular faces in one of two ways: Work out the area of each rectangle separately, length × width. Multiply the perimeter of the end face by the length of the prism.
  • Sum the areas of all the faces.

What formula is used for surface area? ›

Surface Area Formula List
ShapeLateral Surface Area (LSA)Total Surface Area (TSA)
Cylinder2πrh2πr(r + h)
Coneπrlπr(l + r)
Sphere4πr24πr2
Hemisphere2πr23πr2
4 more rows
Feb 19, 2024

What is the formula for the total surface area of a square prism? ›

Surface area of a square prism = 4 × (s × h) = 4sh, where, s is the length of the side of the square and h is the height of the square prism.

What is the formula for the total surface area of a triangular prism? ›

Therefore, it is calculated using the formula, Total Surface Area = (Perimeter of the base × Length) + (2 × Base Area); or TSA = (S1 + S2 + S2)L + bh; where: b is the bottom edge of the base triangle, h is the height of the base triangle, L is the length of the prism and.

What is the formula for the surface area of a trapezoidal prism? ›

The surface area of a trapezoidal prism can be given with this formula: (b1+b2)h + PH. In this formula, "b1" and "b2" stand for the length of the bases of the trapezoid. The height of the trapezoid is "h". The perimeter of the trapezoid is "P", and "H" is the height of the prism.

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