medium difficulty5 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.

In one line: Quadrilateral area depends on the family of the four-sided figure.

Practice This Concept

Understand it

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.

Example

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

Formula and rule

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

See it worked out

Follow the example line by line, then use the same method on new questions.

Worked example

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

Method you can reuse

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

Sketch it in your answer

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

Check yourself

Answer the question in your head before opening the answer.

Try it yourself

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

Think first, then show answer

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

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.

Don't mix this up

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

Exam tip

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

Write it in the exam

Each point is worth about one mark. Write point 1 for a 1-mark question and keep adding points as the marks go up.

How CBSE asks it

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

1
Enough for 1 mark
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
Add for 2 marks
Example: A trapezium with parallel sides 12 cm and 8 cm and height 5 cm has area = 1/2 × (12 + 8) × 5 = 50 cm².
3
Add for 3 marks
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.

MCQ Quiz

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