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Points to Remember: Mensuration | Mathematics (Maths) Class 8 PDF Download
Important Formulae
1. Area of a parallelogram = Base x Height
2. Area of a triangle = 1/2 x Base x Height
3. Area of a trapezium = 1/2 x [Sum of parallel sides] x Height
4. Area of a rhombus = 1/2 x Product of diagonals
5. Surface area of
(i) a cuboid = 2[lb + bh + hl]
(ii) a cube = 6a2
(iii) a cylinder = 2πr(r + h)
6. Volume of
(i) cuboid = l x b x h
(ii) cube = l3
(iii) cylinder = πr2h
- 1 m3 = 1000 litres
- A square, a rectangle, a trapezium, a rhombus, a parallelogram, a triangle, a circle, etc., are plane figures and the surfaces enclosed by their boundaries are called areas. We have formulae to find their areas. The perimeter is the distance around a figure. The plane figures are also called 2-D shapes. The solids such as cubes, cuboids, and cylinders are called 3-D shapes. Faces bound a 3-D shape. These faces can be rectilinear curved or both.
Note:
I. All angles of a regular polygon have equal degree measures.
II. All sides of a regular polygon are equal in length.
Solved Examples
Q1. The length and breadth of a rectangle are 10 cm and 8 cm respectively. Find its perimeter if the length and breadth are (i) doubled (ii) halved.
Ans:
Length of the rectangle = 10 cm
Breadth of the rectangle = 8 cm
(i) When they are doubled,
l = 10 × 2 = 20 cm
and b = 8 × 2 = 16 cm
Perimeter = 2(l + b) = 2(20 + 16) = 2 × 36 = 72 cm
(ii) When they are halved,
l = 10/2 = 5 cm
b = 8/2 = 4 cm
Perimeter = 2(l + b) = 2(5 + 4) = 2 × 9 = 18 cmQuestion for Points to Remember: MensurationTry yourself:Q2. If the lateral surface of the cylinder is 500 cm² and its height is 10 cm, then find the radius of its base.
View Solution
Q3. A horse is tethered by a rope 10 m long at a point. Find the area of the region where it can graze (π = 3.14)
Solution: The area of the region the horse can graze is circular with a radius equal to the length of the rope.
The area of the circle is given by πr²
= 3.14 × 10²
= 3.14 × 100
=314
Hence the area of the region the horse can graze is 314 cm².
Question for Points to Remember: MensurationTry yourself:What is the perimeter of a rectangle if its length is 12 cm and its breadth is 8 cm?
View Solution
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FAQs on Points to Remember: Mensuration - Mathematics (Maths) Class 8
| 1. What are the basic formulas used in mensuration for finding the area and volume of common geometric shapes? |  |
Ans. The basic formulas in mensuration include:
- Area of a rectangle = length × breadth
- Area of a square = side × side
- Area of a triangle = (1/2) × base × height
- Area of a circle = π × radius²
- Volume of a cube = side³
- Volume of a rectangular prism = length × breadth × height
- Volume of a cylinder = π × radius² × height
| 2. How do you calculate the surface area of a cube? | |
Ans. The surface area of a cube can be calculated using the formula:
Surface Area = 6 × (side)².
This means you take the length of one side of the cube, square it, and then multiply that by 6 since a cube has six equal faces.
| 3. What is the difference between area and perimeter in mensuration? | |
Ans. Area refers to the amount of space inside a shape, measured in square units (like square meters), while perimeter is the total distance around the outside of a shape, measured in linear units (like meters). For example, for a rectangle, the area is found using length × breadth, and the perimeter is calculated as 2 × (length + breadth).
| 4. Can you explain how to find the volume of a cylinder? | |
Ans. To find the volume of a cylinder, use the formula:
Volume = π × radius² × height.
First, square the radius, multiply it by π (approximately 3.14), and then multiply that result by the height of the cylinder.
| 5. What is the importance of mensuration in real life? | |
Ans. Mensuration is important in real life as it helps in various fields such as architecture, engineering, and construction, where accurate measurements of area and volume are crucial. It is also used in everyday situations like calculating the amount of paint needed to cover a wall or determining the size of furniture that can fit in a room.
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