Mensuration: SGT
Mensuration
Basic Measurements
| Quantity | Common Units | Standard Conversion |
|---|---|---|
| Length | mm, cm, m, km | 1 m = 100 cm |
| Weight | mg, g, kg | 1 kg = 1000 g |
| Capacity | ml, L | 1 L = 1000 ml |
| Area | cm², m² | 1 m² = 10000 cm² |
Memory: Area is the surface covered by a shape, always written in square units.
Tip: Always check unit match before solving numerical problems.
Symmetry
| Type | Meaning | Example |
|---|---|---|
| Line Symmetry | Shape divides into equal halves by a line | Square, Rectangle |
| Rotational Symmetry | Shape looks same after rotation | Regular Hexagon |
Memory: A square has 4 lines of symmetry and rotational symmetry of order 4.
Tip: If a shape matches itself before full 360° rotation, it has rotational symmetry.
Perimeter
| Shape | Formula |
|---|---|
| Triangle | a + b + c |
| Square | 4 × side |
| Rectangle | 2(l + b) |
| Circle | 2πr |
Memory: Perimeter is the total boundary length of a shape.
Tip: Always use π = 22/7 or 3.14 depending on question.
Properties of Special Quadrilaterals
| Shape | Key Properties |
|---|---|
| Parallelogram | Opposite sides equal & parallel |
| Rhombus | All sides equal |
| Rectangle | All angles 90° |
| Square | All sides equal and all angles 90° |
Memory: Diagonals of a parallelogram bisect each other.
Tip: Mid-point theorem applies only for triangles.
Area of Plane Figures
| Figure | Formula |
|---|---|
| Triangle | (1/2) × base × height |
| Rectangle | l × b |
| Square | side² |
| Circle | πr² |
| Trapezium | (1/2) (sum of parallel sides) × height |
Memory: Area depends on perpendicular height, not slant side.
Tip: Divide irregular shapes into smaller regular shapes for easy calculation.
Surface Area and Volume of 3D Shapes
| Solid | Surface Area | Volume |
|---|---|---|
| Cube | 6a² | a³ |
| Cuboid | 2(lb + bh + hl) | l × b × h |
| Cylinder | 2πr(h + r) | πr²h |
| Sphere | 4πr² | (4/3)πr³ |
| Cone | πr(l + r) | (1/3)πr²h |
Memory: Slant height (l) is used for cone surface area.
Tip: Check if curved or total surface area is asked.
Volume and Capacity
| Concept | Explanation |
|---|---|
| Volume | Space occupied by a solid |
| Capacity | Maximum liquid a container can hold |
| Conversion | 1 cm³ = 1 ml |
Memory: 1000 cm³ = 1 litre.
Tip: Use volume concept in tank and water storage problems.
Combination of Solids
| Type | Method |
|---|---|
| Surface Area | Add only visible surfaces |
| Volume | Add volumes of individual solids |
| Recasting | Volume before = volume after |
Memory: In melting and recasting, volume always remains constant.
Tip: Clearly identify overlapping surfaces before calculation.