# All Mensuration Formulas for 2D and 3D Shapes (With PDF)

Mensuration is the branch of mathematics that deals with the measurement of geometric shapes/figures and their parameters like length, area, volume, lateral surface area, etc. In this post, we will explore all the mensuration formulas for 2D and 3D shapes, Mensuration Definition, providing you with a clear understanding of their calculations and applications.

## Definition of Mensuration

Mensuration is a branch of mathematics that deals with the measurement of geometric figures and their parameters like length, area, volume, lateral surface area, etc. These Mensuration shapes exist either in 2D and 3D. Let’s learn the difference between 2D and 3D shapes.

### Differences Between 2D and 3D shapes

Mensuration Formulas PDF

## Mensuration Formulas for 2D and 3D Shapes

Here below we will provide all the all the mensuration formulas for 2D and 3D shapes.

## All the Maths Formulas for Mensuration

Mensuration Formula for Rectangle :

• Area = l×b
• Perimeter = 2(l+b)

Mensuration Formula for Square :

• Area = a×a
• Perimeter = 4a

Mensuration Formula for Parallelogram :

• Area = l×h
• Perimeter = 2(l+b)

Mensuration Formula for Triangle :

• Area =12×b×h or √s(s−a)(s−b)(s−c),where s=a+b+c2

Mensuration Formula for Right angle Triangle :

• Area =12×b×h
• Perimeter = Sum of all sides

Mensuration Formula for Isosceles right angle triangle :

• Area = 12×b×h
• Perimeter = 2a+d, where d=a√2

Mensuration Formula for Equilateral Triangle :

• Area = √34a2
• Perimeter = 3a

Mensuration Formula for Trapezium :

• Area =12h×(sum of parallel sides)\$
• Perimeter = Sum of all sides

Mensuration Formula for Rhombus :

• Area = 12×d1×d2 where d1,d2 are diagonals
• Perimeter = 4l

• Area = 12×b×h

Mensuration Formula for Kite :

• Area = 12×d1×d2, where d1,d2 are diagonals
• Perimeter = 2× Sum on non-adjacent sides

Mensuration Formula for Circle :

• Area = πr2
• Circumference = 2πr
• Area of sector of a circle = θπr2360∘

Mensuration Formula for Frustum :

• Curved surface area = πh(r1+r2)
• Surface area = π(r21+h(r1+r2)+r22)

Mensuration Formula for Cube :

• Volume: V = a3
• Lateral surface area = 4a2
• Surface Area: S = 6a2
• Diagonal (d) = √3a

Mensuration Formula for Cuboid :

• Volume of cuboid: lbh
• Total surface area = 2(lb+bh+hl)
• Length of diagonal = √(l2+b2+h2)

Mensuration Formula for Right Circular Cylinder :

• Volume of Cylinder = πr2h
• Lateral Surface Area (LSA or CSA) = 2πrh
• Total Surface Area = TSA = 2πr(r+h)
• Volume of hollow cylinder = πrh(R2–r2)

Mensuration Formula for Right Circular cone :

• Volume = 13πr2h
• Curved surface area: CSA= πrl
• Total surface area = TSA = πr(r+l)

Mensuration Formula for Sphere:

• Volume: V = 43πr3
• Surface Area: S = 4πr2

Mensuration Formula for Hemisphere :

• Volume = 23πr3
• Curved surface area(CSA) = 2πr2
• Total surface area = TSA = 3πr2

Mensuration Formula for Prism :

• Volume = Base area × h
• Lateral Surface area = perimeter of the base × h

Mensuration Formula for Pyramid:

• Volume of a right pyramid = 13 × area of the base × height.
• Area of the lateral faces of a right pyramid = 12 × perimeter of the base × slant height.
• Area of whole surface of a right pyramid = area of the lateral faces + area of the base.

Mensuration Formula for Tetrahedron :

• Area of its slant sides = 3a2sqrt34
• Area of its whole surface = √3a2
• Volume of the tetrahedron = √212a3

Mensuration Formula for Regular Hexagon :

• Area = 3×√3a22
• Perimeter = 6a

## Mensuration Solved Problems: Mensuration Formulas

### Problem 1: Calculating the Area of a Triangle

Question: Find the area of a triangle with a base of 10 inches and height of 8 inches.

Solution: Need to apply formula to calculate the area of a triangle is: A = (1/2) * base * height.

Substituting the given values into the formula, we have:

A = (1/2) * 10 * 8 = 40 square inches.

Therefore, the area of the triangle is 40 square inches.

### Problem 2: Determining the Perimeter of a Rectangle

Question: Find the perimeter of a rectangle with a length of 12 meters and a width of 8 meters.

Solution: Need to apply formula to calculate the perimeter of a rectangle is: P = 2 * (length + width).

Substituting the given values into the formula, we have:

P = 2 * (12 + 8) = 2 * 20 = 40 meters.

Therefore, the perimeter of the rectangle is 40 meters.

### Problem 3: Calculating the Volume of a Cylinder

Question: Find the volume of a cylinder with a radius of 5 centimeters and a height of 10 centimeters.

Solution: Need to apply formula to calculate the volume of a cylinder is: V = π * radius^2 * height.

Substituting the given values into the formula, we have:

V = π * 5^2 * 10 = 250π cubic centimeters.

Therefore, the volume of the cylinder is 250π cubic centimeters.

### Problem 4: Finding the Surface Area of a Sphere

Question: Find the surface area of a sphere with a radius of 7 inches.

Solution: Need to apply formula to calculate the surface area of a sphere is: SA = 4 * π * radius^2.

Substituting the given value into the formula, we have:

SA = 4 * π * 7^2 = 4 * 49π = 196π square inches.

Therefore, the surface area of the sphere is 196π square inches.

### Problem 5: Determining the Volume of a Cone

Question: Find the volume of a cone with a radius of 6 centimeters and a height of 12 centimeters.

Solution: Need to apply formula to calculate the volume of a cone is: V = (1/3) * π * radius^2 * height.

Substituting the given values into the formula, we have:

V = (1/3) * π * 6^2 * 12 = 144π cubic centimeters.

Therefore, the volume of the cone is 144π cubic centimeters.

### Problem 6: Calculating the Area of a Trapezoid

Question: Find the area of a trapezoid with a base of 10 inches, a top length of 6 inches, and a height of 4 inches.

Solution: Need to apply formula to calculate the area of a trapezoid is: A = (1/2) * (base1 + base2) * height.

Substituting the given values into the formula, we have:

A = (1/2) * (10 + 6) * 4 = 8 * 4 = 32 square inches.

Therefore, the area of the trapezoid is 32 square inches.

### Problem 7: Determining the Circumference of a Circle

Question: Find the circumference of a circle with a diameter of 12 meters.

Solution: Need to apply formula to calculate the circumference of a circle is: C = π * diameter.

Substituting the given value into the formula, we have:

C = π * 12 = 12π meters.

Therefore, the circumference of the circle is 12π meters.

### Problem 8: Calculating the Surface Area of a Cube

Question: Find the surface area of a cube with a side length of 5 centimeters.

Solution: Need to apply formula to calculate the surface area of a cube is: SA = 6 * side^2.

Substituting the given value into the formula, we have:

SA = 6 * 5^2 = 6 * 25 = 150 square centimeters.

Therefore, the surface area of the cube is 150 square centimeters.

### Problem 9: Finding the Volume of a Prism

Question: Find the volume of a rectangular prism with a length of 8 inches, a width of 6 inches, and a height of 4 inches.

Solution: Need to apply formula to calculate the volume of a rectangular prism is: V = length * width * height.

Substituting the given values into the formula, we have:

V = 8 * 6 * 4 = 192 cubic inches.

Therefore, the volume of the rectangular prism is 192 cubic inches.

### Problem 10: Calculating the Area of a Circle

Question: Find the area of a circle with a radius of 9 inches.

Solution: Need to apply formula to calculate the area of a circle is: A = π * radius^2.

Substituting the given value into the formula, we have:

A = π * 9^2 = 81π square inches.

Therefore, the area of the circle is 81π square inches.