Grade 8
  1. Number Systems  1.1. Rational Numbers  1.2. Irrational Numbers  1.3. Real Numbers  1.4. Properties of Real Numbers  1.4.1. Commutative Property  1.4.2. Associative Property  1.4.3. Distributive Property  1.5. Representation on the Number Line  1.6. Operations on Real Numbers  1.6.1. Addition and Subtraction  1.6.2. Multiplication and Division  1.7. Rationalization  1.8. Exponents and Powers  1.9. Square Roots and Cube Roots
  2. Algebra  2.1. Algebraic Expressions  2.2. Identities and Simplification  2.2.1. Multiplying Binomials  2.2.2. Using Algebraic Identities  2.3. Factorization  2.3.1. Common Factors  2.3.2. Factorization by Grouping  2.3.3. Factorization of Trinomials  2.3.4. Special Products  2.4. Linear Equations in One Variable  2.4.1. Solving Linear Equations  2.4.2. Word Problems on Linear Equations
  3. Geometry  3.1. Understanding Quadrilaterals  3.1.1. Properties of Quadrilaterals  3.1.2. Types of Quadrilaterals  3.1.2.1. Parallelogram  3.1.2.2. Rectangle  3.1.2.3. Square  3.1.2.4. Rhombus  3.1.2.5. Trapezium  3.2. Constructions  3.2.1. Constructing Quadrilaterals  3.2.2. Constructing Bisectors  3.2.3. Constructing Angles  3.2.4. Constructing Triangles  3.3. Symmetry and Transformations  3.3.1. Reflection  3.3.2. Rotation  3.3.3. Translation  3.3.4. Symmetry in Patterns
  4. Mensuration  4.1. Area and Perimeter  4.1.1. Perimeter of Polygons  4.1.2. Area of Triangles  4.1.3. Area of Quadrilaterals  4.1.4. Area of Circles  4.2. Surface Area and Volume  4.2.1. Cubes  4.2.2. Cuboids  4.2.3. Cylinders  4.2.4. Cones  4.2.5. Spheres
  5. Data Handling  5.1. Organizing Data  5.2. Frequency Distribution Tables  5.3. Graphical Representation of Data  5.3.1. Bar Graphs  5.3.2. Histograms  5.3.3. Pie Charts  5.3.4. Line Graphs (added)  5.4. Probability  5.4.1. Introduction to Probability  5.4.2. Experimental Probability
  6. Coordinate Geometry  6.1. Cartesian Plane  6.2. Plotting Points  6.3. Coordinate System  6.4. Distance Between Points  6.5. Applications of Coordinate Geometry
  7. Introduction to Graphs  7.1. Linear Graphs  7.2. Applications of Graphs  7.3. Distance-Time Graphs  7.4. Speed-Time Graphs
  8. Comparing Quantities  8.1. Ratio and Proportion  8.2. Percentage  8.2.1. Increase and Decrease Percent  8.2.2. Discount in Percentage  8.2.3. Profit and Loss in Percentage  8.2.4. Simple Interest  8.2.5. Compound Interest
  9. Exponents and Powers  9.1. Laws of Exponents  9.2. Negative Exponents  9.3. Standard Form  9.4. Applications of Exponents
  10. Introduction to Squares and Square Roots  10.1. Properties of Square Numbers  10.2. Finding Square Roots  10.2.1. Prime Factorization Method  10.2.2. Division Method  10.3. Estimating Square Roots
  11. Introduction to Cubes and Cube Roots  11.1. Properties of Cube Numbers  11.2. Finding Cube Roots  11.2.1. Prime Factorization Method in Finding Cube Roots

Grade 8 ↓


Mensuration


Measurement is a branch of mathematics that deals with the measurement of geometric shapes and figures. It involves calculating length, area, and volume. Measurement is a very practical subject as it helps us understand and figure out measurements in real life. Whenever you want to know how much space a room has, or how much water a tank can hold, you are using measurement.

Basic terms and concepts

Before we delve deeper into the different shapes and their measurements, it is important to understand some basic terms and concepts:

  • Perimeter: The perimeter is the total length around a shape. For example, if you have a fence around your garden, the length of that fence is the perimeter.
  • Area: Area is the space that a shape covers. This is especially useful for things like flooring or painting, where you want to know how much material is needed to cover the surface.
  • Volume: Volume is the space that a 3-dimensional object contains. It is useful in understanding how much an object can contain, such as water in a tank or air in a balloon.

Perimeter of common shapes

The perimeter is the distance around a two-dimensional shape. Let's take a look at some common shapes:

Perimeter of a square

A square has four equal sides. If the length of one side is s, then the perimeter P of the square is given by:

P = 4 × s
S S S S

For example, if each side of the square is 5 cm, then the perimeter is:

P = 4 × 5 = 20 cm

Perimeter of a rectangle

The opposite sides of a rectangle are equal. If the length is l and the width is w, then the perimeter P is:

P = 2 × (l + w)
l w l w

If the length is 8 cm and breadth is 3 cm, then the perimeter is:

P = 2 × (8 + 3) = 2 × 11 = 22 cm

Area of common shapes

Area of a square

The area of a square with side length s is:

A = s²
S

If each side of the square is 5 cm, then the area is:

A = 5² = 25 cm²

Area of a rectangle

The area of a rectangle of length l and width w is:

A = l × w
l w

If the length is 8 cm and breadth is 3 cm, then the area is:

A = 8 × 3 = 24 cm²

Volume of 3D shapes

Volume is the measure of the space occupied by a three-dimensional object.

Volume of a cube

A cube has six square faces of equal size. If the side length of each square is s, then the volume V of the cube is:

V = s³
S

For example, if each side of the cube is 4 cm, then the volume is:

V = 4³ = 64 cm³

Volume of a rectangular prism

A rectangular prism is like a rectangle with a depth of 1. If the length is l, the width is w, and the height is h, then the volume V is:

V = l × w × h

If the length is 6 cm, breadth 3 cm and height 2 cm, then the volume is:

V = 6 × 3 × 2 = 36 cm³

Circle measurement

Circumference of a circle

The circumference is the distance around a circle. If the radius is r, then the circumference C is:

C = 2 × π × r
R

If the radius of the circle is 7 cm, then the circumference is approximately:

C = 2 × 3.14 × 7 ≈ 43.96 cm

Area of a circle

The area of a circle of radius r is:

A = π × r²
R

If the radius is 7 cm, the area is approximately:

A = 3.14 × 7² ≈ 153.86 cm²

Practical applications of mensuration

Measurement is extremely useful in everyday life. Whether you are calculating the amount of wrapping paper needed for a gift or determining the paint needed for a wall, measurement comes in handy.

Wall painting

Imagine you want to paint a wall 10 meters long and 3 meters high. To find out how much paint you need, you first calculate the area of the wall:

A = l × h = 10 × 3 = 30 meters²

Now, knowing the area, you can decide how much paint you need to buy based on the paint coverage specifications. If one can of paint covers 5 m², you will need:

Number of paint cans = Area / Coverage per can = 30 / 5 = 6 cans

Garden fence

You want to fence around a rectangular garden that is 20 m long and 15 m wide. To find the required length of the fence, calculate the perimeter:

P = 2 × (l + w) = 2 × (20 + 15) = 2 × 35 = 70 meters

Conclusion

Measurement is an essential part of mathematics that allows us to understand the world in terms of length, area, and volume. From determining the amount of paint needed for a wall to estimating the amount of water in a swimming pool, understanding measurement can simplify many practical tasks. By mastering these concepts, you can solve real-world problems with confidence and accuracy.


Grade 8 → 4


U
username
0%
completed in Grade 8

← Prev (3.3.4)
Symmetry in Patterns
Next (4.1) →
Area and Perimeter

Comments 



Mensuration

https://www.buddymath.com/g8/4?bmal=en