CBSE Class 8 Maths Chapter 14: Area — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 14: Area from the NCERT Class 8 Mathematics textbook. Each question has four options - read both the Assertion (A) and Reason (R) carefully before selecting your answer.
How to attempt Assertion & Reason questions:
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
(a) Both A and R are true, and R is the correct explanation of A.
(b) Both A and R are true, but R is NOT the correct explanation of A.
(c) A is true, but R is false.
(d) A is false, but R is true.
Assertion & Reason Questions
1
Assertion (A): Area measures the amount of two-dimensional region covered.
Reason (R): It can be expressed as the number of unit squares needed to cover the region without overlap or gaps.
Reason (R): It can be expressed as the number of unit squares needed to cover the region without overlap or gaps.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Unit squares provide the measurement standard.
2
Assertion (A): The area of a rectangle is length times width.
Reason (R): The perimeter of a rectangle is twice the sum of length and width.
Reason (R): The perimeter of a rectangle is twice the sum of length and width.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both formulas are true, but perimeter does not explain area.
3
Assertion (A): Rectangles with the same perimeter can have different areas.
Reason (R): Equal perimeter always forces equal area.
Reason (R): Equal perimeter always forces equal area.
Answer: (c)
A is true, but R is false. For example, 1 by 5 and 2 by 4 both have perimeter 12 but different areas.
4
Assertion (A): A region with larger perimeter always has larger area.
Reason (R): Perimeter measures boundary length, while area measures surface coverage.
Reason (R): Perimeter measures boundary length, while area measures surface coverage.
Answer: (d)
A is false, but R is true. Neither measurement alone determines the other.
5
Assertion (A): A diagonal divides a rectangle into two congruent triangles of equal area.
Reason (R): The two triangles together exactly make the rectangle.
Reason (R): The two triangles together exactly make the rectangle.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Congruence and complete coverage give each half the rectangle's area.
6
Assertion (A): The area of a triangle is one-half times base times corresponding height.
Reason (R): Any side may be chosen as base if its perpendicular height is used.
Reason (R): Any side may be chosen as base if its perpendicular height is used.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but choice of another base does not itself derive the formula.
7
Assertion (A): The height used in a triangle's area formula is perpendicular to the chosen base.
Reason (R): Any sloping side can replace the perpendicular height without changing the calculation.
Reason (R): Any sloping side can replace the perpendicular height without changing the calculation.
Answer: (c)
A is true, but R is false. The corresponding altitude must meet the base line at a right angle.
8
Assertion (A): Two triangles with equal bases always have equal areas regardless of height.
Reason (R): Triangle area depends on both base and corresponding height.
Reason (R): Triangle area depends on both base and corresponding height.
Answer: (d)
A is false, but R is true. Equal base alone is insufficient.
9
Assertion (A): Triangles on the same base and between the same parallels have equal area.
Reason (R): They share the same base length and perpendicular distance between the parallels.
Reason (R): They share the same base length and perpendicular distance between the parallels.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The formula gives identical one-half base times height.
10
Assertion (A): The area of a parallelogram is base times corresponding height.
Reason (R): Opposite sides of a parallelogram are parallel.
Reason (R): Opposite sides of a parallelogram are parallel.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but parallel sides alone do not supply the numerical height and base calculation.
11
Assertion (A): The area of a parallelogram is base times perpendicular height.
Reason (R): Its slant side always equals the perpendicular height.
Reason (R): Its slant side always equals the perpendicular height.
Answer: (c)
A is true, but R is false. The slant side generally differs from the altitude.
12
Assertion (A): A parallelogram and rectangle with equal base and height have different areas.
Reason (R): Both have area equal to base times height.
Reason (R): Both have area equal to base times height.
Answer: (d)
A is false, but R is true. Their areas are equal.
13
Assertion (A): A polygon can be divided into non-overlapping triangles to find its area.
Reason (R): The polygon's area equals the sum of the component triangle areas.
Reason (R): The polygon's area equals the sum of the component triangle areas.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Additivity of area justifies triangulation.
14
Assertion (A): A rhombus is a parallelogram, so base times corresponding height gives its area.
Reason (R): A square is also a special rhombus.
Reason (R): A square is also a special rhombus.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the square classification does not explain the general rhombus formula.
15
Assertion (A): The area of a trapezium is one-half times the sum of parallel sides times height.
Reason (R): The factor one-half is never used in the trapezium formula.
Reason (R): The factor one-half is never used in the trapezium formula.
Answer: (c)
A is true, but R is false. The stated area formula includes the factor one-half.
16
Assertion (A): The area of a trapezium depends only on its two parallel sides and not on height.
Reason (R): Changing the perpendicular distance between the parallel sides changes its area.
Reason (R): Changing the perpendicular distance between the parallel sides changes its area.
Answer: (d)
A is false, but R is true. Height is an essential factor.
17
Assertion (A): Two congruent trapeziums can be arranged into a parallelogram.
Reason (R): The parallelogram then has base a + b and height h, so one trapezium has half its area.
Reason (R): The parallelogram then has base a + b and height h, so one trapezium has half its area.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. This construction derives the trapezium formula.
18
Assertion (A): Converting a shape by cutting and rearranging without overlap can preserve area.
Reason (R): The lengths of all individual boundaries must also remain in the same positions.
Reason (R): The lengths of all individual boundaries must also remain in the same positions.
Answer: (c)
A is true, but R is false. Area is preserved even though boundary arrangement and perimeter may change.
19
Assertion (A): Doubling every linear dimension of a figure multiplies its area by four.
Reason (R): A triangle's area is one-half base times height.
Reason (R): A triangle's area is one-half base times height.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both are true, but the triangle formula does not explain area scaling for every figure.
20
Assertion (A): One square metre equals 100 square centimetres.
Reason (R): Since 1 m = 100 cm, 1 square metre equals 10000 square centimetres.
Reason (R): Since 1 m = 100 cm, 1 square metre equals 10000 square centimetres.
Answer: (d)
A is false, but R is true. Both length dimensions are multiplied by 100.
❓ Frequently Asked Questions
What is covered in CBSE Class 8 Maths Chapter 14 Area?
This chapter covers all key topics from Area as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 8 board exam preparation covering the complete syllabus.
Are these CBSE Class 8 Maths Assertion & Reason updated for 2026-27?
Yes, all content at eBookPublisher is updated as per the latest 2026-27 CBSE syllabus.
How many chapters are in CBSE Class 8 Maths?
All chapters of CBSE Class 8 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
Can I study Area online for free?
Yes, complete Assertion & Reason for Area is available free at eBookPublisher. Study online directly — no download needed.
Where can I get a complete Assertion & Reason book for CBSE Class 8 Maths?
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