C
CraftExam
high importancemedium8 min

Area of Quadrilaterals

The area of a quadrilateral is the surface enclosed by a four-sided figure, found using the formula matching its shape and given conditions.

Practice This Concept

Learn the concept

Student-friendly explanation

Different quadrilaterals need different formulas. A rectangle uses length and breadth, a parallelogram uses base and height, a trapezium uses parallel sides and height, and a rhombus can use diagonals.

How to write this in exams

  1. 1

    Start with the exact idea

    The area of a quadrilateral is the surface enclosed by a four-sided figure, found using the formula matching its shape and given conditions.

  2. 2

    Then show how to use it

    Name the quadrilateral, list the given measures, choose the matching formula, substitute only required values, and write square units.

  3. 3

    Add one concrete example

    A trapezium with parallel sides 12 cm and 8 cm and height 5 cm has area = 1/2 × (12 + 8) × 5 = 50 cm².

  4. 4

    Avoid this incomplete answer

    For a parallelogram, base × slant side is wrong unless the slant side is also the perpendicular height, which it usually is not.

Definition

The area of a quadrilateral is the surface enclosed by a four-sided figure, found using the formula matching its shape and given conditions.

Example

A trapezium with parallel sides 12 cm and 8 cm and height 5 cm has area = 1/2 × (12 + 8) × 5 = 50 cm².

Rule to remember

Rectangle: l × b; square: a²; parallelogram: base × height; trapezium: 1/2(a + b)h; rhombus: 1/2 d1d2.

Memory hook

Quadrilateral area depends on the family of the four-sided figure.

Examples and method

Worked example

A rhombus has diagonals 16 cm and 10 cm. Area = 1/2 × 16 × 10 = 80 cm².

Method to apply

Name the quadrilateral, list the given measures, choose the matching formula, substitute only required values, and write square units.

Diagram support

Mark parallel sides, perpendicular height, or diagonals according to the formula being used.

How CBSE asks it

Exam questions may mix extra side lengths with the needed height or ask for area from a labelled diagram.

Avoid common mistakes

Common confusion

Students often use slant side instead of perpendicular height for a parallelogram or trapezium.

Common wrong answer

For a parallelogram, base × slant side is wrong unless the slant side is also the perpendicular height, which it usually is not.

Exam tip

First identify the quadrilateral type and the required perpendicular height or diagonals.

Quick check

What is the area of a parallelogram with base 15 cm and perpendicular height 6 cm?

The area is 15 × 6 = 90 cm² because a parallelogram uses base multiplied by perpendicular height.

Answer writing and exam use

1-mark answer

The area of a quadrilateral is the surface enclosed by a four-sided figure, found using the formula matching its shape and given conditions.

2-mark answer

The area of a quadrilateral is the surface enclosed by a four-sided figure, found using the formula matching its shape and given conditions. Rectangle: l × b; square: a²; parallelogram: base × height; trapezium: 1/2(a + b)h; rhombus: 1/2 d1d2. A trapezium with parallel sides 12 cm and 8 cm and height 5 cm has area = 1/2 × (12 + 8) × 5 = 50 cm².

3-mark answer

Different quadrilaterals need different formulas. A rectangle uses length and breadth, a parallelogram uses base and height, a trapezium uses parallel sides and height, and a rhombus can use diagonals. Rectangle: l × b; square: a²; parallelogram: base × height; trapezium: 1/2(a + b)h; rhombus: 1/2 d1d2. A rhombus has diagonals 16 cm and 10 cm. Area = 1/2 × 16 × 10 = 80 cm². Exam questions may mix extra side lengths with the needed height or ask for area from a labelled diagram. For a parallelogram, base × slant side is wrong unless the slant side is also the perpendicular height, which it usually is not.
MCQ Quiz

Practice this concept with focused MCQs

Open the concept quiz intro first, review the test details, and then start a focused MCQ set from this concept only. Instant score and answer review are live now.

10 MCQs5 MinutesInstant Results
Practice This Concept

Help improve this page

Found something confusing, incorrect, or missing?

Practice This Concept