NCERT Class 8 Maths Chapter 14
Area
NCERT Class 8 Maths Chapter 14 (Ganita Prakash Part 2) provides a comprehensive treatment of area — how to measure the two-dimensional space enclosed by various shapes including triangles, quadrilaterals, and circles. This CBSE chapter connects geometry with arithmetic, developing formulae from first principles and applying them to complex composite figures. Students solve practical problems involving land measurement, floor plans, and surface areas.
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Key Terms
- Area
- The measure of the two-dimensional space enclosed within a boundary of a shape; measured in square units (cm², m², etc.).
- Perimeter
- The total length of the boundary of a two-dimensional shape; measured in linear units (cm, m, etc.).
- Base and Height
- In area calculations, the base is any chosen side of a figure, and the height (altitude) is the perpendicular distance from the base to the opposite vertex or side.
- Parallelogram Area
- Area = Base × Height (perpendicular height, not slant height); the height must be perpendicular to the base.
- Trapezium Area
- Area = ½ × (sum of parallel sides) × height = ½(a + b)h, where a and b are the lengths of the parallel sides.
- Circle Area
- Area = πr², where r is the radius and π ≈ 3.14159; the circumference (perimeter) of a circle = 2πr.
- Composite Figure
- A shape made up of two or more basic geometric shapes; its area is found by adding or subtracting the areas of the component shapes.
Frequently Asked Questions
What are the area formulas Class 8 Maths?▾
Key area formulas in NCERT Class 8: Rectangle = length × breadth. Square = side². Triangle = ½ × base × height. Parallelogram = base × height. Trapezium = ½ × (a+b) × h (a, b = parallel sides, h = height). Circle = πr². Rhombus = ½ × d₁ × d₂ (d₁, d₂ = diagonals). These formulas are derived and applied in Chapter 14.
What is the difference between area and perimeter Class 8 NCERT?▾
Perimeter is the total distance around the outside boundary of a shape (measured in linear units: cm, m). Area is the amount of surface enclosed inside the boundary (measured in square units: cm², m²). A large perimeter does not always mean a large area — a very thin rectangle can have a large perimeter but a tiny area.
How do you find the area of a parallelogram Class 8?▾
Area of parallelogram = Base × Height, where the height is the perpendicular distance between the two parallel bases (not the slant side length). For example, a parallelogram with base 8 cm and perpendicular height 5 cm has area = 8 × 5 = 40 cm². A rectangle is a special parallelogram where height equals the shorter side.
How do you find the area of a trapezium Class 8 Maths?▾
Area of trapezium = ½ × (a + b) × h, where a and b are the two parallel sides and h is the perpendicular height between them. Example: parallel sides 6 cm and 10 cm, height 4 cm; Area = ½ × (6+10) × 4 = ½ × 16 × 4 = 32 cm². This formula comes from treating the trapezium as two triangles.
How do you find the area of composite figures Class 8 NCERT?▾
For composite (combined) figures: (1) Identify the basic shapes that make up the figure, (2) Calculate the area of each basic shape separately, (3) Add the areas together (or subtract for cut-out regions). Example: An L-shaped room can be divided into two rectangles; find each area and add. This approach is used extensively in Class 8 word problems.
What is the area of a circle and how is it derived Class 8?▾
Area of circle = πr² (π ≈ 3.14 or 22/7; r = radius). It can be derived by dividing a circle into many thin sectors and rearranging them to approximate a rectangle with length πr (half the circumference) and width r, giving area ≈ πr × r = πr². Circumference = 2πr. Example: circle with radius 7 cm; Area = (22/7) × 7² = 154 cm².
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