# NCERT Class 8 Mathematics Chapter 14 Area: Summary, Concepts, and Revision Notes | SwaVid

This chapter, 'Area', from the NCERT Class 8 Mathematics textbook 'Ganita Prakash-II', builds upon your previous knowledge of calculating areas of basic...

Canonical: https://swavid.com/maths/class/8/chapter/area

Source: https://swavid.com/maths/class/8/chapter/area

# Area

## Concepts in this chapter

## The ideas this chapter keeps returning to

## Where this chapter usually trips people up

## Find the gaps before this chapter finds them for you.

## Related chapters

### Understanding Area and its Measurement

Chapter 14 · Class 8 Mathematics

This chapter, 'Area', from the NCERT Class 8 Mathematics textbook 'Ganita Prakash-II', builds upon your previous knowledge of calculating areas of basic shapes. It introduces methods to find the area of more complex two-dimensional figures such as trapeziums, general quadrilaterals, rhombuses, and various polygons. The focus is on understanding the specific formulas and decomposition techniques required for these shapes.

Your study route

Key topics

Area is the measure of the two-dimensional space enclosed by a closed figure. It is always expressed in square units, such as square centimetres (cm²) or square metres (m²). This chapter builds upon prior knowledge of areas of basic shapes like squares, rectangles, triangles, and parallelograms to explore more complex figures.

Example

Implicitly introduced in the chapter's opening, building on prior knowledge.

Watch out

Confusing area with perimeter. Perimeter is the length of the boundary, while area is the space inside.

Area is the measure of the two-dimensional space enclosed by a closed figure. It is always expressed in square units, such as square centimetres (cm²) or square metres (m²). This chapter builds upon prior knowledge of areas of basic shapes like squares, rectangles, triangles, and parallelograms to explore more complex figures.

Tap the card for an example

Example

Implicitly introduced in the chapter's opening, building on prior knowledge.

Why it matters

Understanding area is fundamental for various practical applications, from calculating the amount of paint needed for a wall to determining the size of a plot of land.

Watch out

Confusing area with perimeter. Perimeter is the length of the boundary, while area is the space inside.

Ask at home

Ask the child to explain the difference between area and perimeter and to name common units for area.

The chapter 'Area' extends previous knowledge of calculating areas to more complex two-dimensional shapes. It introduces methods for finding the area of a trapezium, defined by its parallel sides and perpendicular height. Students learn to calculate the area of a general quadrilateral by dividing it into two triangles using one of its diagonals. A specific formula is provided for the area of a rhombus, utilizing the lengths of its diagonals. Furthermore, the chapter demonstrates how to determine the area of any polygon by decomposing it into simpler, non-overlapping shapes like triangles and trapeziums, a technique crucial for practical applications such as surveying land. This systematic approach ensures comprehensive understanding and application of area concepts for various geometric figures.

Chapter summary

The chapter 'Area' extends previous knowledge of calculating areas to more complex two-dimensional shapes. It introduces methods for finding the area of a trapezium, defined by its parallel sides and perpendicular height. Students learn to calculate the area of a general quadrilateral by dividing it into two triangles using one of its diagonals. A specific formula is provided for the area of a rhombus, utilizing the lengths of its diagonals. Furthermore, the chapter demonstrates how to determine the area of any polygon by decomposing it into simpler, non-overlapping shapes like triangles and trapeziums, a technique crucial for practical applications such as surveying land. This systematic approach ensures comprehensive understanding and application of area concepts for various geometric figures.

What you should learn

Keep these close

Area is the measure of the surface enclosed by a closed figure, expressed in square units.

The area of a trapezium is calculated as (1/2) × (sum of parallel sides) × height.

The height of a trapezium must be the perpendicular distance between its parallel sides.

The area of a general quadrilateral can be found by dividing it into two triangles using one of its diagonals.

For a general quadrilateral, Area = (1/2) × d × (h1 + h2), where 'd' is the diagonal and 'h1', 'h2' are perpendiculars to it.

The area of a rhombus is given by (1/2) × d1 × d2, where d1 and d2 are the lengths of its diagonals.

Polygons can be decomposed into simpler shapes like triangles and trapeziums to calculate their total area.

When decomposing a polygon, ensure all parts are covered without overlap and all necessary measurements are identified.

Field diagrams represent irregular plots of land, and their areas are calculated using the polygon decomposition method.

Always pay attention to units and ensure consistency in calculations (e.g., all measurements in cm or m).

Common confusions

It is easy to think

Confusing the height of a trapezium with one of its non-parallel sides.

The clearer idea

The height of a trapezium is always the perpendicular distance between its two parallel sides.

It is easy to think

Attempting to use the (1/2)d1d2 formula for any quadrilateral.

The clearer idea

The formula (1/2)d1d2 is specifically for rhombuses (and kites) where diagonals are perpendicular. For general quadrilaterals, divide into two triangles.

It is easy to think

Incorrectly dividing a polygon, leading to missing sections or overlapping areas.

The clearer idea

Systematically divide the polygon into non-overlapping triangles and trapeziums, ensuring every part of the polygon is included exactly once.

It is easy to think

Not understanding which measurements correspond to bases, heights, or diagonals in complex diagrams.

The clearer idea

Carefully label all given measurements and identify their geometric role (e.g., perpendicular height, parallel side, diagonal) before applying formulas.

Before you push ahead

Most stuck chapters trace back to one earlier idea. Check the prerequisites first, or let SwaVid adapt this chapter to the way your child learns.

Keep exploring Class 8

Source

- Apply the formula to calculate the area of a trapezium.
- Determine the area of a general quadrilateral by dividing it into two triangles.
- Calculate the area of a rhombus using the lengths of its diagonals.
- Find the area of various polygons by decomposing them into simpler shapes like triangles and trapeziums.
- Solve problems involving the area of trapeziums, general quadrilaterals, rhombuses, and polygons in different contexts.
- Apply the formula to calculate the area of a trapezium.
- Determine the area of a general quadrilateral by dividing it into two triangles.
- Calculate the area of a rhombus using the lengths of its diagonals.
- Find the area of various polygons by decomposing them into simpler shapes like triangles and trapeziums.
- Solve problems involving the area of trapeziums, general quadrilaterals, rhombuses, and polygons in different contexts.
- NCERT Class 8 Mathematics textbook: Ganita Prakash-II : Chapter 14: Area

## Key Links

- [NCERT Mathematics](https://swavid.com/maths)
- [Class 8](https://swavid.com/maths/class/8)
- [Start with concepts](https://swavid.com/maths/class/8/chapter/area)
- [Check a prerequisite](https://swavid.com/learning-debt-identifier)
- [Concepts](https://swavid.com/maths/class/8/chapter/area)
- [Practice](https://swavid.com/maths/class/8/chapter/area/practice-questions)
- [NCERT Solutions](https://swavid.com/maths/class/8/chapter/area/ncert-solutions)
- [Find the gaps before this chapter](https://swavid.com/learning-debt-identifier)
- [Learn this chapter adapted to you](https://swavid.com/learning-style-test)
- [Previous chapter 13 . Algebra Play](https://swavid.com/maths/class/8/chapter/algebra-play)
- [All Class 8 chapters](https://swavid.com/maths/class/8)
- [13 Algebra Play Understanding Algebraic Expressions · Combining Algebraic Expressions Open chapter](https://swavid.com/maths/class/8/chapter/algebra-play)
- [12 Tales by Dots and Lines The Cartesian Plane: Your Map for Numbers · Coordinates and Plotting Points: Finding Your Way Open chapter](https://swavid.com/maths/class/8/chapter/tales-by-dots-and-lines)
- [11 Exploring Some Geometric Themes Polyhedrons and Their Classification · Euler's Formula for Polyhedrons Open chapter](https://swavid.com/maths/class/8/chapter/exploring-some-geometric-themes)
- [NCERT Class 8 Mathematics textbook: Ganita Prakash-II](https://ncert.nic.in/textbook/pdf/hegp207.pdf)