Mensuration Math Formulas for 2D and 3D Shapes Notes

Mensuration Notes

Table of Contents

1. Definition of Mensuration
2. Important Terms in Mensuration
3. Mensuration Formulas
• 2D Shapes
• 3D Shapes
4. Difference Between 2D and 3D Shapes
5. Mensuration Notes in Details

Mensuration

➥ Mensuration is the branch of mathematics that deals with the measurement of geometric figures like 2D shapes (areas) and 3D objects (surface area and volume).

Important Terms in Mensuration

1. Perimeter: The total length of the boundary of a closed figure.
2. Area: The space enclosed within a 2D shape.
3. Volume: The space occupied by a 3D object.
4. Lateral/Curved Surface Area (LSA/CSA): The area of all the sides of a 3D object excluding the top and bottom.
5. Total Surface Area (TSA): The total area covered by the outer surfaces of a 3D object.

Mensuration Formulas

2D Shapes

Shape	Area	Perimeter	Diagonal	Diagram
Square	Side2	4 × Side	√2 × Side
Rectangle	L × B	2 × (L + B)	√(L2 + B2)
Triangle	½ × Base × Height	Sum of all sides	N/A
Circle	πr2	2πr	√(2 × r2)
Semi-Circle	½ × πr2	πr + 2r	√(r2 + r2)

3D Shapes

Shape	Volume	Curved Surface Area (CSA)	Total Surface Area (TSA)	Diagram
Cube	Side3	4 × Side2	6 × Side2
Cuboid	L × B × H	2(LB + HL)	2(LB + BH + HL)
Cylinder	πr2h	2πrh	2πr(r + h)
Cone	⅓πr2h	πrl	πr(r + l)
Sphere	4/3πr3	N/A	4πr2
Hemisphere	2/3πr3	2πr2	3πr2

Difference Between 2D and 3D Shapes

Feature	2D Shapes	3D Shapes
Definition	Have only length and breadth.	Have length, breadth, and height.
Area/Volume	Only area is measured.	Both surface area and volume are measured.
Example	Square, Triangle, Circle	Cube, Cylinder, Sphere

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Mensuration (2-D & 3-D) Notes in Details

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