Mensuration 8 Maths — Revision Notes
Mensuration deals with the measurement of lengths, areas, and volumes of geometric figures. These concepts are applied in construction, engineering, and da
TL;DR: Mensuration deals with the measurement of lengths, areas, and volumes of geometric figures. These concepts are applied in construction, engineering, a…
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Mensuration deals with the measurement of lengths, areas, and volumes of geometric figures. These concepts are applied in construction, engineering, and da
Perimeter and Area of Quadrilaterals
- Perimeter is the total distance around a closed figure
- Area is the amount of surface enclosed by a figure
- Rectangle: perimeter equals 2(length plus width); area equals length times width
- Square: perimeter equals 4 times side; area equals side squared
- Parallelogram: area equals base times height
- Rhombus: area equals half times product of diagonals
Area of Triangle and Trapezium
- Triangle: area equals one-half times base times height
- Trapezium: area equals one-half times sum of parallel sides times height
- For triangle with sides a, b, c use Heron's formula with semi-perimeter s
- Heron's formula: area equals square root of s(s-a)(s-b)(s-c)
- Right triangle: area equals one-half times product of two perpendicular sides
Surface Area of Solids
- Cube: surface area equals 6 times side squared
- Cuboid: surface area equals 2(length times width plus width times height plus height times length)
- Cylinder: surface area equals 2 pi r squared plus 2 pi r h
- Sphere: surface area equals 4 pi r squared
- Cone: surface area equals pi r squared plus pi r l, where l is slant height
Volume of Solids
- Volume is the amount of space occupied by a three-dimensional figure
- Cube: volume equals side cubed
- Cuboid: volume equals length times width times height
- Cylinder: volume equals pi r squared h
- Sphere: volume equals four-thirds pi r cubed
- Cone: volume equals one-third pi r squared h
Practical Applications
- Land measurement uses area calculations for property valuation
- Container volume determines capacity for liquids and solids
- Painting requires surface area to determine paint quantity needed
- Construction uses volume and surface area for material estimation
- Garden design uses perimeter and area for planning layouts
Key Terms
- Perimeter: Total distance around the boundary of a two-dimensional figure
- Area: Measure of the surface enclosed by a two-dimensional figure
- Volume: Measure of space occupied by a three-dimensional figure
- Surface Area: Total area of all faces of a three-dimensional solid
Frequently Asked Questions
What is the difference between surface area and volume?
Surface area measures the total area of the outer surface of a 3D object. Volume measures the space inside the object.
When should Heron's formula be used?
Heron's formula is used to find the area of a triangle when all three side lengths are known but the height is not given.
More 8 Maths Revision Notes
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →