Prism Formula

Prism can be defined as a polyhedron that has two polygon-shaped bases opposite to each other and some lateral surfaces. Prism has smooth polished surfaces which refract light. Bases of the prism are generally triangular in shape and lateral surfaces have rectangular or parallelogram shapes. 

Properties of Prism

• Two bases of a prism are parallel to each other and are mostly triangular in shape.
• Faces other than bases (base and top) are called lateral faces.
• Prism has the property of refracting light.
• White light can be split into seven rainbow colours by using prism at certain angles.
• Lateral surfaces are of a parallelogram or rectangular shape.

Prism Formula 

Surface area of Prism = (2×BaseArea) + Surface Area of Lateral Surfaces

Types of Prism

There are different types of prism: 

Triangular Prism

It is the simplest type of prism with two triangular faces which can be called base and top, and three lateral faces that are rectangular in shape.

Area of base = 1/2 × (base) × (height) = 1/2 × (b) × (h)

Total Surface Area = Area of two bases + Area of 3 lateral surfaces

                              = 2 × (1/2×(base)×(height)) + 3 × length×breadth

                              = b × h + 3 × a × b

Rectangular Prism

It is a type of prism with two rectangular faces which can be called a base and top, and four lateral faces which are rectangular in shape. It looks like a cuboid in shape.

Area of base = (breadth) × (height)

Total Surface Area = Area of two bases + Area of 4 lateral surfaces

                              = 2×(breadth)×(height) + 2×length×breadth + 2×length×height

Pentagonal Prism

It is a type of prism with two pentagonal faces which can be called base and top, and five lateral faces which are rectangular in shape.

Area of base = 5/2×a×b

Total Surface Area = Area of two bases + Area of 5 lateral surfaces

                             = 2×(5/2×a×b) + 5×b×h

                             = (5×a×b) + 5×b×h

Hexagonal Prism

It is a type of prism with two hexagonal faces which can be called base and top, and six lateral faces which are rectangular in shape.

Area of base = 3×a×b

Total Surface Area = Area of two bases + Area of 6 lateral surfaces

                             = 2×(3×a×b) + 6×b×h

                             = (6×a×b) + 6×b×h

Sample Questions

Question 1: Find the area of the triangular prism which has a length of 10 cm, a breadth of 6 cm and a height of 2 cm.

Solution: 

Given length (a) = 10 cm, breadth (b) = 6 cm, and height (h) = 2 cm.

Area of triangular prism

Total Surface Area = Area of two bases + Area of 3 lateral surfaces

                  = 2×(1/2×(base)×(height)) + 3×length×breadth

                  = b×h + 3×a×b

                 = 6×2 + 3×10×6

                 = 12 + 180

                 = 192 cm²

Question 2: Find the area of the rectangular prism which has a length of 10 cm, a breadth of 6 cm and a height of 2 cm.

Solution: 

Given length (a) = 10 cm, breadth (b) = 6 cm, and height (h) = 2 cm.

Area of the rectangular prism

Total Surface Area = Area of two bases + Area of 4 lateral surfaces

                 = 2×(breadth)×(height) + 2×length×breadth +  2×length×height

                 = 2×6×2 + 2×10×6 + 2×10×2

                 = 24 + 120 + 40

                 = 184 cm²

Question 3: Find the area of the pentagonal prism which has a = 5 cm, breadth of 6 cm and a height of 10 cm.

Solution: 

Given (a) = 5 cm, breadth (b) = 6 cm, and height (h) = 10 cm.

Area of a pentagonal prism

Total Surface Area = Area of two bases + Area of 5 lateral surfaces

                 = 2×(5/2×a×b) + 5×b×h

                 = (5×a×b) + 5×b×h

                 = (5×5×6) + 5×6×10

                 = 150 + 300

                 = 450 cm²

Question 4: Find the area of the hexagonal prism which has a = 5 cm, breadth of 6 cm and a height of 10 cm.

Solution: 

Given (a) = 5 cm, breadth (b) = 6 cm, and height (h) = 10 cm.

Area of a hexagonal prism

Total Surface Area = Area of two bases + Area of 6 lateral surfaces

                 = 2×(3×a×b) + 6×b×h

                 = (6×a×b) + 6×b×h

                 = (6×5×6) + 6×6×10

                 = 180 + 360

                 = 540 cm²

Question 5: Find the lateral surface area of hexagonal prism which has a breadth of 6 cm and a height of 10 cm.

Solution: 

Given breadth (b) = 6 cm, and height (h) = 10 cm.

Area of 6 lateral surfaces = 6×b×h

                                        = 6×6×10

                                        = 360 cm²