This MCQ module is based on: 6.2 Area
TOPIC 21 OF 41
6.2 Area
🎓 Class 6
Mathematics
CBSE
Theory
Ch 6 — Perimeter and Area
⏱ ~15 min
🌐 Language: [gtranslate]
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This mathematics assessment will be based on: 6.2 Area
Targeting Class 6 level in Mensuration, with Basic difficulty.
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6.2 Area
We've studied the amount of boundary a shape has — its perimeter. Now we move on to the amount of surface a closed figure covers. This quantity is called the area? of the figure.
Definition
The area of a closed plane figure is the measure of the region it encloses. Area is measured in square units — square centimetres (cm²), square metres (m²), square kilometres (km²), etc.
Area of a Rectangle
Imagine laying 1-cm square tiles inside a rectangle 5 cm long and 3 cm wide. You can fit 5 tiles along one row, and 3 such rows — so 5 × 3 = 15 tiles cover the whole rectangle. Each tile is a 1 cm² unit, so the rectangle's area is 15 cm².
Tiling a 5 cm × 3 cm rectangle with 1 cm² unit squares.
Formula
Area of a rectangle = length × breadth i.e. \(A = L \times B\).Area of a square = side × side i.e. \(A = s^2\).
Example — Akshi's Floor
A floor is 5 m long and 4 m wide. A square carpet of side 3 m is laid on the floor. Find the area of the floor that is not carpeted.
Floor area = 5 × 4 = 20 m². Carpet area = 3 × 3 = 9 m². Uncovered area = 20 − 9 = 11 m².
The square carpet (blue) sits on a rectangular floor (yellow).
Example — Four Square Flower Beds
Four square flower beds each of side 4 m are on a rectangular plot of length 12 m and breadth 10 m. Find the area of the remaining part of the plot.
Plot area = 12 × 10 = 120 m². Total bed area = 4 × (4 × 4) = 64 m². Remaining = 120 − 64 = 56 m².
Figure it Out (Section 6.2)
Q1. The area of a rectangular garden 25 m long is 300 m². What is the width?
Width = 300 ÷ 25 = 12 m.
Q2. Tiling a rectangular plot of land 500 m long and 200 m wide costs ₹8 per square metre. Find the total cost.
Area = 500 × 200 = 1,00,000 m². Cost = 1,00,000 × 8 = ₹8,00,000.
Q3. A rectangular coconut grove is 100 m long and 50 m wide. If each coconut tree requires 25 m², what is the maximum number of trees that can be planted in this grove?
Area = 100 × 50 = 5000 m². Max trees = 5000 ÷ 25 = 200 trees.
Q4. By splitting the figure into rectangles, find its area (all measurements in metres).
(a) Step-shape with pieces 3×1, 3×2, 1×4 etc.
(b) Plus-shape with 3×3 centre and 3×1 arms.
(a) Step-shape with pieces 3×1, 3×2, 1×4 etc.
(b) Plus-shape with 3×3 centre and 3×1 arms.
(a) Splitting gives total = 25 sq m. (b) Splitting gives total = 9 sq m. Break the figure into non-overlapping rectangles, find each area, and add.
6.3 Area of a Triangle
Draw any rectangle on paper and cut it along one of its diagonals. You get two triangles that stack exactly on top of each other — they have the same area.
Rectangle ABCD cut along diagonal AC gives two equal-area triangles.
Inference
Area of a right triangle formed by a diagonal of a rectangle = \(\tfrac{1}{2} \times\) area of the rectangle = \(\tfrac{1}{2} \times L \times B\).
Example — Triangle inside Rectangle ABCD
Consider rectangle ABCD with two points E on DC and F on AB, making red and blue triangles. Using grid/diagonal-splitting:
Area of triangle BAD = \(\tfrac{1}{2}\) × area of rectangle ABCD.
Triangle ABE lies across two smaller rectangles AFED and FBCE. Its area = \(\tfrac{1}{2}\) × area of AFED + \(\tfrac{1}{2}\) × area of FBCE = \(\tfrac{1}{2}\) × area of ABCD.
Triangle ABE spans two sub-rectangles; its area is half of ABCD.
Teacher's Note: A diagonal of a rectangle is a line segment joining two opposite vertices. It splits the rectangle into two congruent triangles that share the diagonal as a common side.
Composite Figures — Splitting
To find the area of an L-shape or plus-shape, split it into rectangles (and triangles), compute each piece, and add up. For example: an L-shape with overall dimensions 5 × 4 with a 2 × 2 corner removed has area 20 − 4 = 16 sq units.
Splitting a composite L-shape into two rectangles A and B.
Activity: Paper-Fold the Diagonal
L3 Apply
Materials: Two identical rectangular sheets of paper (any size), ruler, pencil, scissors
Predict: When you cut a rectangle along its diagonal, will the two triangles you get have equal areas? Why?
- Take one rectangle and measure its length L and breadth B.
- Draw one diagonal and cut along it with scissors.
- Place one triangle on top of the other — do they match?
- Compute \(L \times B\). Then compute \(\tfrac{1}{2}\times L \times B\). Which is the triangle's area?
- Extension: cut the SECOND rectangle along the OTHER diagonal and compare.
The two triangles stack perfectly — they are congruent. Each has area \(\tfrac{1}{2} L B\). This is the foundation of the triangle-area formula you will meet in later classes.
Competency-Based Questions
Scenario: Raghav is designing a rectangular parking lot 40 m long and 25 m wide. He plans a triangular flower-bed in one corner (using half of a 10 m × 6 m rectangle), and a square lawn of side 8 m elsewhere. Paving the rest costs ₹120/m².
Q1. Calculate the total area of the parking lot.
L3 ApplyArea = 40 × 25 = 1000 m².
Q2. Analyse — what area is left for paving after subtracting the flower-bed and lawn?
L4 AnalyseFlower-bed (triangular) = ½ × 10 × 6 = 30 m². Lawn = 8 × 8 = 64 m². Paved = 1000 − 30 − 64 = 906 m².
Q3. Evaluate the paving cost.
L5 EvaluateCost = 906 × 120 = ₹1,08,720.
Q4. Create — redesign the lawn as a rectangle with the SAME area (64 m²) but a perimeter less than the square's perimeter. Is it possible? Justify.
L6 CreateSquare perimeter = 32 m. For a rectangle with area 64 m², the perimeter is minimised precisely when it is a square (8 × 8). Any other rectangle with the same area (e.g. 4 × 16) will have a greater perimeter. So it is not possible. Among all rectangles of fixed area, the square has the smallest perimeter.
Assertion–Reason Questions
A: The area of a rectangle of length 8 cm and breadth 5 cm is 40 cm².
R: Area of a rectangle equals length times breadth.
R: Area of a rectangle equals length times breadth.
Answer: (a).
A: The two triangles formed by a diagonal of any rectangle have equal area.
R: A diagonal of a rectangle divides it into two congruent right triangles.
R: A diagonal of a rectangle divides it into two congruent right triangles.
Answer: (a). Congruent triangles always have equal area.
A: Two rectangles with the same perimeter must have the same area.
R: Area is determined by length × breadth, not by perimeter alone.
R: Area is determined by length × breadth, not by perimeter alone.
Answer: (d). A is false — rectangles 1×5 and 2×4 both have perimeter 12 but areas 5 and 8.
Frequently Asked Questions — Perimeter and Area
What is Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool in NCERT Class 6 Mathematics?
Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool is a key concept covered in NCERT Class 6 Mathematics, Chapter 6: Perimeter and Area. This lesson builds the student's foundation in the chapter by explaining the core ideas with worked examples, definitions, and step-by-step methods aligned to the CBSE curriculum.
How do I solve problems on Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool step by step?
To solve problems on Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool, follow the NCERT method: identify the given quantities, choose the relevant formula or theorem, substitute values carefully, and simplify. Class 6 exercises gradually increase in difficulty — start with solved NCERT examples before attempting exercise questions, and always verify your answer by substitution or diagram.
What are the most important formulas for Chapter 6: Perimeter and Area?
The essential formulas of Chapter 6 (Perimeter and Area) are listed in the chapter summary and highlighted throughout the lesson in formula boxes. Memorise them and practise at least 2–3 problems per formula. CBSE board exams frequently test direct application as well as combined use of multiple formulas from this chapter.
Is Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool important for the Class 6 board exam?
Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool is part of the NCERT Class 6 Mathematics syllabus and appears in CBSE board exams. Questions typically include short-answer, long-answer, and competency-based items. Review the NCERT examples, exercise questions, and previous-year board problems on this topic to prepare confidently.
What mistakes should students avoid in Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool?
Common mistakes in Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool include skipping steps, misapplying formulas, sign errors, and losing track of units. Write each step clearly, double-check algebraic manipulations, and re-read the question after solving to verify that your answer matches what was asked.
Where can I find more NCERT practice questions on Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool?
End-of-chapter NCERT exercises for Part 2 — Area of Rectangles, Squares & Triangles | Class 6 Maths | MyAiSchool cover all difficulty levels tested in CBSE exams. After completing them, try the examples again without looking at the solutions, attempt the NCERT Exemplar questions for Chapter 6, and solve at least one previous-year board paper to consolidate your understanding.
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