FORMULAS OF MENSURATION
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Answer:
A branch of mathematics that talks about the length, volume, or area of different geometric shapes is called Mensuration. These shapes exist in 2 dimensions or 3 dimensions. Let’s learn the difference between the two.
Differences Between 2D and 3D shapes
2D Shape 3D Shape
If a shape is surrounded by three or more straight lines in a plane, then it is a 2D shape. If a shape is surrounded by a no. of surfaces or planes then it is a 3D shape.
These shapes have no depth or height. These are also called solid shapes and unlike 2D they have height or depth.
These shapes have only two dimensions say length and breadth. These are called Three dimensional as they have depth (or height), breadth and length.
We can measure their area and Perimeter. We can measure their volume, CSA, LSA or TSA.
Mensuration in Maths- Important Terminologies
Let’s learn a few more definitions related to this topic.
Terms Abbreviation Unit Definition
Area A m2 or cm2 The area is the surface which is covered by the closed shape.
Perimeter P cm or m The measure of the continuous line along the boundary of the given figure is called a Perimeter.
Volume V cm3 or m3 The space occupied by a 3D shape is called a Volume.
Curved Surface Area CSA m2 or cm2 If there’s a curved surface, then the total area is called a Curved Surface area. Example: Sphere
Lateral Surface area LSA m2 or cm2 The total area of all the lateral surfaces that surrounds the given figure is called the Lateral Surface area.
Total Surface Area TSA m2 or cm2 The sum of all the curved and lateral surface areas is called the Total Surface area.
Square Unit – m2 or cm2 The area covered by a square of side one unit is called a Square unit.
Cube Unit – m3 or cm3 The volume occupied by a cube of one side one unit
Mensuration Formulas
Now let’s learn all the important mensuration formulas involving 2D and 3D shapes. Using this mensuration formula list, it will be easy to solve the mensuration problems. Students can also download the mensuration formulas list PDF from the link given above. In general, the most common formulas in mensuration involve surface area and volumes of 2D and 3D figures.
Mensuration Formulas For 2D Shapes
Shape Area (Square units) Perimeter (units) Figure
Square a2 4a Mensuration Formula for Square
Rectangle l × b 2 ( l + b) Mensuration Formula for Rectange
Circle πr2 2 π r Mensuration Formula for Circle
Scalene Triangle √[s(s−a)(s−b)(s−c)],
Where, s = (a+b+c)/2
a+b+c Mensuration Formula for Scalene triangle
Isosceles Triangle ½ × b × h 2a + b Mensuration Formula for Isosceles triangle
(√3/4) × a2 3a Mensuration Formula for Equilateral triangle
Right Angle Triangle ½ × b × h b + hypotenuse + h Mensuration Formula for Right triangle
Rhombus ½ × d1 × d2 4 × side Mensuration Formula for Rhombus
Parallelogram b × h 2(l+b) Mensuration Formula for Parallelogram
Trapezium ½ h(a+c) a+b+c+d Mensuration Formula for TrapeziumSwipe left
Mensuration Formulas for 3D Shapes
Shape Volume (Cubic units) Curved Surface Area (CSA) or Lateral Surface Area (LSA) (Square units) Total Surface Area (TSA) (Square units) Figure
Cube a3 LSA = 4 a2 6 a2 Mensuration Formula for Cube
Cuboid l × b × h LSA = 2h(l + b) 2 (lb +bh +hl) Mensuration Formula for Cuboid
Sphere (4/3) π r3 4 π r2 4 π r2 Mensuration Formula for Sphere
Hemisphere (⅔) π r3 2 π r 2 3 π r 2 Mensuration Formula for Hemisphere
Cylinder π r 2 h 2π r h 2πrh + 2πr2 Mensuration Formula for Cylinder
Cone (⅓) π r2 h π r l πr (r + l) Mensuration Formula for ConeSwipe left
Mensuration Problems
Question: Find the area and perimeter of a square whose side is 5 cm.
Solution:
Given:
Side = a = 5 cm
Area of a square = a2 square units
Substitute the value of “a” in the formula, we get
Area of a square = 52
A = 5 x 5 = 25
Therefore, the area of a square = 25 cm2
The perimeter of a square = 4a units
P = 4 x 5 =20
Therefore, the perimeter of a square = 20 cm.
Answer:
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