Class 8 Mathematics – Mensuration

1. Introduction

• Mensuration is the branch of mathematics that deals with measuring geometric figures in terms of length, area, and volume.

• It helps in real-life applications like construction, packaging, and material estimation.

Key Concept:

• Area → space inside a shape

• Surface Area → total area covering a 3D object

• Volume → space occupied by a 3D object

2. Area of Trapezium

• A trapezium is a quadrilateral with one pair of parallel sides.

• The area represents the space enclosed inside the trapezium.

• Key Concept:

  • Area depends on the length of parallel sides and the height (perpendicular distance between them).

• Applications:

  • Land measurement, architecture, and designing irregular plots.

3. Surface Area of Solids

• Surface area is the total area covering the exterior of a 3D solid.

• Solids considered: Cube, Cuboid, Cylinder, Sphere, Cone, Pyramid.

Key Concept:

• Surface area includes all faces, curved surfaces, or circular surfaces depending on the solid.

• Applications:

  • Painting walls, wrapping gifts, packaging, construction.

Notes:

• For objects with flat faces → add areas of all faces.

• For curved objects → include curved surface area plus bases (if any).

4. Volume of Solids

• Volume is the space occupied by a 3D object.

• Solids considered: Cube, Cuboid, Cylinder, Sphere, Cone, Pyramid.

Key Concept:

• Volume is important for storage, containers, liquids, and materials.

• Unit of volume is cubic unit (like cubic cm, cubic m).

• Volume helps in calculating capacity and material requirements.

5. Applications of Mensuration

1. Daily life: Measuring rooms, furniture, swimming pools, tanks.

2. Construction: Estimating materials needed (cement, bricks, paint).

3. Packaging: Boxes, bottles, and containers.

4. Engineering & Architecture: Designing solid shapes and structures.

6. Key Points to Remember

• Mensuration deals with area, surface area, and volume.

• Trapezium: Area depends on parallel sides and height.

• Surface Area: Total area covering the outside of 3D solids.

• Volume: Space occupied by the solid itself.

• Always visualize the shape to understand what measurements are needed.

• Useful in real-life applications like construction, packaging, and design.