Mensuration
What is Mensuration?
The total distance around the outside of a two-dimensional shape.
Key formula / rule: Area of Rectangle
Key points
- To be able to calculate the perimeter and area of common 2D shapes.
- To be able to calculate the volume and surface area of common 3D shapes.
- To apply mensuration formulas to solve practical problems.
- To interpret and solve problems involving composite shapes.
Common exam trap
Confusing area with perimeter.
Definitions
- Term
Perimeter
- Meaning
The total distance around the outside of a two-dimensional shape.
- Term
Area
- Meaning
The amount of two-dimensional space a shape occupies.
- Term
Volume
- Meaning
The amount of three-dimensional space an object occupies.
- Term
Surface Area
- Meaning
The total area of the outer surfaces of a three-dimensional object.
- Term
Composite Shape
- Meaning
A shape made up of two or more simpler geometric shapes.
Learning objectives
To be able to calculate the perimeter and area of common 2D shapes.
To be able to calculate the volume and surface area of common 3D shapes.
To apply mensuration formulas to solve practical problems.
To interpret and solve problems involving composite shapes.
Formulae
- Name
Area of Rectangle
- Note
where l is length and b is breadth.
- Expression
A = l × b
- Name
Area of Square
- Note
where s is the side length.
- Expression
A = s²
- Name
Area of Circle
- Note
where r is the radius. π (π) is approximately 22/7 or 3.14.
- Expression
A = πr²
- Name
Perimeter of Rectangle
- Note
Sum of all sides.
- Expression
P = 2(l + b)
- Name
Perimeter of Square
- Note
Sum of all sides.
- Expression
P = 4s
- Name
Circumference of Circle
- Note
The boundary length of a circle.
- Expression
C = 2πr
- Name
Volume of Cuboid
- Note
where l, b, h are length, breadth, and height.
- Expression
V = l × b × h
- Name
Volume of Cube
- Note
where s is the side length.
- Expression
V = s³
- Name
Volume of Cylinder
- Note
where r is the radius and h is the height.
- Expression
V = πr²h
- Name
Volume of Sphere
- Note
where r is the radius.
- Expression
V = (4/3)πr³
Prerequisites
Basic arithmetic operations (addition, subtraction, multiplication, division).
Understanding of basic geometric shapes (square, rectangle, circle, triangle, cube, cuboid, cylinder, sphere, cone).
Familiarity with basic algebraic concepts and variables.
Common mistakes
Confusing area with perimeter.
Using incorrect formulas for specific shapes.
Unit conversion errors (e.g., cm to m).
Calculation errors in applying formulas.
Misinterpreting composite shapes.
Keywords
Mensuration
Geometry
Area
Volume
Perimeter
Surface Area
Shapes
Formulas
Measurement
2D
3D
Practice preview
A cube has a total surface area of 294 sq cm. What is the length of its side?…
medium
A rectangular field has a length of 25 meters and a width of 12 meters. What is the area of the field?…
easy
A cylindrical water tank has a volume of 924 cubic meters. If the radius of its base is 7 meters, what is the height of the tank? (Use pi = 22/7)…
medium