CBSE Class 9 Maths Chapter 6: Measuring Space: Perimeter and Area — Assertion & Reason
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The following Assertion and Reason questions are based on Chapter 6: Measuring Space: Perimeter and Area from the NCERT Class 9 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): The perimeter of a plane shape is the total length around its boundary.
Reason (R): It can be measured by tracing the entire border once and adding the lengths covered.
Reason (R): It can be measured by tracing the entire border once and adding the lengths covered.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The complete boundary length is precisely what perimeter measures.
2
Assertion (A): A square of side a has perimeter 4a.
Reason (R): A circle of radius r has area pi r^2.
Reason (R): A circle of radius r has area pi r^2.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both formulas are correct, but the area of a circle does not explain the perimeter of a square.
3
Assertion (A): The circumference of a circle of radius r is 2 pi r.
Reason (R): Doubling the radius makes the circumference four times as large.
Reason (R): Doubling the radius makes the circumference four times as large.
Answer: (c)
A is true, but R is false. Circumference is directly proportional to radius, so doubling r only doubles it.
4
Assertion (A): The ratio of circumference to diameter changes when the size of a circle changes.
Reason (R): For every circle, the ratio C/D is the constant pi.
Reason (R): For every circle, the ratio C/D is the constant pi.
Answer: (d)
A is false, but R is true. Similarity of circles keeps this ratio fixed regardless of scale.
5
Assertion (A): The circumference of a circle can be written as C = pi D.
Reason (R): Pi is defined as the constant ratio C/D.
Reason (R): Pi is defined as the constant ratio C/D.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Multiplying both sides of C/D = pi by D gives the formula.
6
Assertion (A): Pi is an irrational number.
Reason (R): Values such as 22/7 and 3.14 are useful approximations to pi.
Reason (R): Values such as 22/7 and 3.14 are useful approximations to pi.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but the existence of approximations does not explain irrationality.
7
Assertion (A): An arc subtending a central angle theta has length 2 pi r x theta/360.
Reason (R): An angle of 180 degrees always corresponds to the full circumference.
Reason (R): An angle of 180 degrees always corresponds to the full circumference.
Answer: (c)
A is true, but R is false. A 180-degree arc is a semicircle and has half the circumference.
8
Assertion (A): Perimeter is expressed in square units because it measures a two-dimensional region.
Reason (R): Perimeter measures length and is therefore expressed in linear units.
Reason (R): Perimeter measures length and is therefore expressed in linear units.
Answer: (d)
A is false, but R is true. Square units are used for area, not boundary length.
9
Assertion (A): The area of a parallelogram equals base multiplied by the corresponding perpendicular height.
Reason (R): A parallelogram can be rearranged into a rectangle with the same base, height, and area.
Reason (R): A parallelogram can be rearranged into a rectangle with the same base, height, and area.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. The rearrangement preserves area and produces the rectangle formula bh.
10
Assertion (A): Rectangles on the same base and between the same parallel lines have equal areas.
Reason (R): The area of a triangle is one-half base multiplied by height.
Reason (R): The area of a triangle is one-half base multiplied by height.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but the triangle formula does not explain the equality of those rectangles.
11
Assertion (A): The area of a parallelogram is base multiplied by its perpendicular height.
Reason (R): The slant side must always be used as the height.
Reason (R): The slant side must always be used as the height.
Answer: (c)
A is true, but R is false. Height is the perpendicular distance between the parallel bases, not generally a sloping side.
12
Assertion (A): The area of a parallelogram depends only on its base and slant side, not on perpendicular height.
Reason (R): Its area is the product of a base and the corresponding perpendicular height.
Reason (R): Its area is the product of a base and the corresponding perpendicular height.
Answer: (d)
A is false, but R is true. Changing the height while keeping base and slant side conditions appropriate can change the area.
13
Assertion (A): A triangle with base b and perpendicular height h has area one-half bh.
Reason (R): Two congruent copies of the triangle can form a parallelogram of area bh.
Reason (R): Two congruent copies of the triangle can form a parallelogram of area bh.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Each triangle occupies half of that parallelogram.
14
Assertion (A): Heron's formula gives the area of a triangle from its three side lengths.
Reason (R): Brahmagupta's formula gives the area of a cyclic quadrilateral from its four side lengths and semiperimeter.
Reason (R): Brahmagupta's formula gives the area of a cyclic quadrilateral from its four side lengths and semiperimeter.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both formulas are correct, but the cyclic-quadrilateral formula does not explain Heron's triangle formula.
15
Assertion (A): Heron's formula is sqrt(s(s - a)(s - b)(s - c)), where s is the semiperimeter.
Reason (R): The formula remains valid for any three positive lengths even when they do not satisfy the triangle inequality.
Reason (R): The formula remains valid for any three positive lengths even when they do not satisfy the triangle inequality.
Answer: (c)
A is true, but R is false. The lengths must form a genuine triangle; otherwise the required area is not defined as a real triangle area.
16
Assertion (A): The area of a circle of radius r is 2 pi r.
Reason (R): The correct area formula is pi r^2.
Reason (R): The correct area formula is pi r^2.
Answer: (d)
A is false, but R is true. The expression 2 pi r gives circumference, not area.
17
Assertion (A): A circle of radius r has area pi r^2.
Reason (R): Scaling the radius by a factor k scales the area by k^2.
Reason (R): Scaling the radius by a factor k scales the area by k^2.
Answer: (a)
Both A and R are true, and R is the correct explanation of A. Substitution gives pi(kr)^2 = k^2 pi r^2.
18
Assertion (A): A sector with central angle theta has area pi r^2 x theta/360.
Reason (R): Pi is an irrational number.
Reason (R): Pi is an irrational number.
Answer: (b)
Both A and R are true, but R is NOT the correct explanation of A. Both statements are true, but the irrationality of pi does not explain how sector area depends on the central angle.
19
Assertion (A): The area of a 180-degree sector is one-half pi r^2.
Reason (R): A 180-degree sector covers the entire circle.
Reason (R): A 180-degree sector covers the entire circle.
Answer: (c)
A is true, but R is false. A 180-degree sector is a semicircle and covers half the circle.
20
Assertion (A): If every linear dimension of a figure is multiplied by k, its area is multiplied only by k.
Reason (R): Scaling all lengths by k multiplies area by k^2.
Reason (R): Scaling all lengths by k multiplies area by k^2.
Answer: (d)
A is false, but R is true. Area has two dimensions, so both independent length factors acquire the scale factor.
❓ Frequently Asked Questions
What is covered in CBSE Class 9 Maths Chapter 6 Measuring Space: Perimeter and Area?
This chapter covers all key topics from Measuring Space: Perimeter and Area as per CBSE 2026-27 syllabus.
Is this Assertion & Reason useful for CBSE board exams?
Yes, designed for CBSE Class 9 board exam preparation covering the complete syllabus.
Are these CBSE Class 9 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 9 Maths?
All chapters of CBSE Class 9 Maths are covered at eBookPublisher with free Assertion & Reason for each chapter.
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