Class 9 CBSE Mathematics — Chapter 6: Measuring Space: Perimeter and Area MCQs with Answers
90 practice questions · 30 Easy · 30 Medium · 30 Hard
Practise the most important Class 9 CBSE Mathematics questions from Chapter 6, "Measuring Space: Perimeter and Area" — 9 separately timed quizzes built from 90 NCERT-aligned multiple-choice questions, with answers and explanations. The set is split into 30 Easy, 30 Medium and 30 Hard, so you can warm up on the fundamentals and then push into the exam-level problems that separate top scorers in CBSE Board exams and the JEE & NEET foundation years.
"Measuring Space: Perimeter and Area" is a chapter that rewards problem-solving speed, formula recall and step-by-step reasoning. Each MCQ on this chapter is timed and uses exam-grade marking (+4 correct, −1 wrong, 0 skipped), training the accuracy-under-pressure that real papers demand. Every question carries a short explanation, so a wrong answer becomes a quick lesson rather than a dead end — the fastest way to close gaps before a test.
Use this chapter as targeted revision: attempt the Easy set first to confirm your basics on Measuring Space: Perimeter and Area, then move to Medium and Hard to test application and problem-solving. Your accuracy, streaks and XP save automatically, and the chapter feeds into your overall Class 9 Mathematics mastery score. 14 sample questions are solved in full below — answer and worked explanation — and signing in free opens all 90.
Key concepts: Measuring Space: Perimeter and Area (Class 9 Mathematics)
Perimeter measures the boundary of a figure and area the space inside it. This chapter gathers the area formulas for the standard polygons, adds Heron's formula for a triangle from its three sides and Brahmagupta's formula for a cyclic quadrilateral, and handles circles, sectors and composite shapes.
- Perimeter
- The total length of the boundary of a closed figure, measured in units of length. For a circle the boundary length is called the circumference.
- Area
- The amount of surface a figure encloses, measured in square units. Doubling every length multiplies the area by four, not by two.
- Area of a triangle (base and height)
- Half the base times the perpendicular height. The height must be perpendicular to the chosen base, not the slanted side.
- Heron's formula
- Gives a triangle's area from its three sides alone, using the semi-perimeter s. Essential when no height is known or easily found.
Class 9 Mathematics Measuring Space: Perimeter and Area MCQs with answers
14 solved questions across the difficulty levels this chapter is graded on — answer and explanation shown for each. The remaining 76 are timed and scored when you sign in.
- Q1Easy
Find the area of a rectangle 12 cm by 5 cm.
A.17 cm²B.34 cm²C.72 cm²D.60 cm²✓ CorrectAnswer: D. 60 cm²
Explanation: Area of a rectangle = length × breadth = 12 × 5 = 60 cm². Adding the sides gives 17 cm², and doubling that (the perimeter) gives 34 cm² — both add the sides instead of multiplying them.
- Q2Easy
Find the area of a rectangle 15 cm by 8 cm.
A.46 cm²B.120 cm²✓ CorrectC.135 cm²D.23 cm²Answer: B. 120 cm²
Explanation: Area of a rectangle = length × breadth = 15 × 8 = 120 cm². Adding the sides gives 23 cm², and doubling that (the perimeter) gives 46 cm² — both add the sides instead of multiplying them.
- Q3Easy
Find the area of a rectangle 9 cm by 7 cm.
A.63 cm²✓ CorrectB.72 cm²C.32 cm²D.16 cm²Answer: A. 63 cm²
Explanation: Area of a rectangle = length × breadth = 9 × 7 = 63 cm². Adding the sides gives 16 cm², and doubling that (the perimeter) gives 32 cm² — both add the sides instead of multiplying them.
- Q4Easy
Find the area of a rectangle 20 cm by 6 cm.
A.52 cm²B.140 cm²C.26 cm²D.120 cm²✓ CorrectAnswer: D. 120 cm²
Explanation: Area of a rectangle = length × breadth = 20 × 6 = 120 cm². Adding the sides gives 26 cm², and doubling that (the perimeter) gives 52 cm² — both add the sides instead of multiplying them.
- Q5Easy
Find the area of a rectangle 11 cm by 10 cm.
A.121 cm²B.42 cm²C.110 cm²✓ CorrectD.21 cm²Answer: C. 110 cm²
Explanation: Area of a rectangle = length × breadth = 11 × 10 = 110 cm². Adding the sides gives 21 cm², and doubling that (the perimeter) gives 42 cm² — both add the sides instead of multiplying them.
- Q6Easy
Find the area of a rectangle 14 cm by 9 cm.
A.46 cm²B.126 cm²✓ CorrectC.140 cm²D.23 cm²Answer: B. 126 cm²
Explanation: Area of a rectangle = length × breadth = 14 × 9 = 126 cm². Adding the sides gives 23 cm², and doubling that (the perimeter) gives 46 cm² — both add the sides instead of multiplying them.
- Q7Medium
Using Heron's formula, find the area of a triangle with sides 13 cm, 14 cm and 15 cm.
A.91 cm²B.90 cm²C.84 cm²✓ CorrectD.42 cm²Answer: C. 84 cm²
Explanation: Heron's formula: s = (13+14+15)/2 = 21 cm. Area = √(s(s−a)(s−b)(s−c)) = √(21×8×7×6) = 84 cm². Using the full perimeter, 42 cm, as s instead of halving it is the usual slip.
- Q8Medium
Using Heron's formula, find the area of a triangle with sides 5 cm, 12 cm and 13 cm.
A.31 cm²B.36 cm²C.33 cm²D.30 cm²✓ CorrectAnswer: D. 30 cm²
Explanation: Heron's formula: s = (5+12+13)/2 = 15 cm. Area = √(s(s−a)(s−b)(s−c)) = √(15×10×3×2) = 30 cm². Using the full perimeter, 30 cm, as s instead of halving it is the usual slip.
- Q9Medium
Using Heron's formula, find the area of a triangle with sides 6 cm, 8 cm and 10 cm.
A.24 cm²✓ CorrectB.25 cm²C.30 cm²D.27 cm²Answer: A. 24 cm²
Explanation: Heron's formula: s = (6+8+10)/2 = 12 cm. Area = √(s(s−a)(s−b)(s−c)) = √(12×6×4×2) = 24 cm². Using the full perimeter, 24 cm, as s instead of halving it is the usual slip.
- Q10Medium
Using Heron's formula, find the area of a triangle with sides 9 cm, 12 cm and 15 cm.
A.55 cm²B.54 cm²✓ CorrectC.60 cm²D.36 cm²Answer: B. 54 cm²
Explanation: Heron's formula: s = (9+12+15)/2 = 18 cm. Area = √(s(s−a)(s−b)(s−c)) = √(18×9×6×3) = 54 cm². Using the full perimeter, 36 cm, as s instead of halving it is the usual slip.
- Q11Medium
Using Heron's formula, find the area of a triangle with sides 8 cm, 15 cm and 17 cm.
A.61 cm²B.66 cm²C.40 cm²D.60 cm²✓ CorrectAnswer: D. 60 cm²
Explanation: Heron's formula: s = (8+15+17)/2 = 20 cm. Area = √(s(s−a)(s−b)(s−c)) = √(20×12×5×3) = 60 cm². Using the full perimeter, 40 cm, as s instead of halving it is the usual slip.
- Q12Hard
A cyclic quadrilateral has sides 3 cm, 3 cm, 4 cm and 4 cm. Using Brahmagupta's formula, find its area.
A.19 cm²B.24 cm²C.12 cm²✓ CorrectD.14 cm²Answer: C. 12 cm²
Explanation: Brahmagupta's formula: s = (3+3+4+4)/2 = 7 cm. Area = √((s−a)(s−b)(s−c)(s−d)) = 12 cm². Using the full perimeter, 14 cm, as s instead of halving it, or stopping before the square root, are the usual slips.
- Q13Hard
A cyclic quadrilateral has sides 3 cm, 3 cm, 5 cm and 5 cm. Using Brahmagupta's formula, find its area.
A.30 cm²B.16 cm²C.22 cm²D.15 cm²✓ CorrectAnswer: D. 15 cm²
Explanation: Brahmagupta's formula: s = (3+3+5+5)/2 = 8 cm. Area = √((s−a)(s−b)(s−c)(s−d)) = 15 cm². Using the full perimeter, 16 cm, as s instead of halving it, or stopping before the square root, are the usual slips.
- Q14Hard
A cyclic quadrilateral has sides 4 cm, 4 cm, 4 cm and 4 cm. Using Brahmagupta's formula, find its area.
A.32 cm²B.23 cm²C.16 cm²✓ CorrectD.17 cm²Answer: C. 16 cm²
Explanation: Brahmagupta's formula: s = (4+4+4+4)/2 = 8 cm. Area = √((s−a)(s−b)(s−c)(s−d)) = 16 cm². Using the full perimeter, 16 cm, as s instead of halving it, or stopping before the square root, are the usual slips.
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Start this chapter free →Measuring Space: Perimeter and Area — FAQs
What are the key concepts in Class 9 Mathematics Measuring Space: Perimeter and Area?+
Perimeter measures the boundary of a figure and area the space inside it. This chapter gathers the area formulas for the standard polygons, adds Heron's formula for a triangle from its three sides and Brahmagupta's formula for a cyclic quadrilateral, and handles circles, sectors and composite shapes. Key ideas include Perimeter, Area, Area of a triangle (base and height), Heron's formula.
What does Class 9 Mathematics Chapter 6 (Measuring Space: Perimeter and Area) cover on XamBaaz?+
It covers 90 NCERT-aligned MCQs on "Measuring Space: Perimeter and Area" — 30 Easy, 30 Medium and 30 Hard — making 9 separately timed quizzes you can sit without ever repeating the same set, each with an instant explanation, suitable for CBSE Board exams and the JEE & NEET foundation years.
Are these "Measuring Space: Perimeter and Area" questions free to practise?+
Yes — sign in with Google to practise "Measuring Space: Perimeter and Area" free. Full unlimited access is ₹999/year (limited-time launch price), with no per-chapter charges.
How should I revise "Measuring Space: Perimeter and Area" for the exam?+
Start with the Easy quiz to confirm your fundamentals, then attempt Medium and Hard for application-level practice. There are 9 separately timed quizzes on this chapter, so you can come back and get a fresh set rather than re-sitting one you have seen. Review each explanation, retry the questions you miss, and track your accuracy on this chapter until it is consistently high.
Are these "Measuring Space: Perimeter and Area" MCQs available with answers?+
Yes. 14 sample questions are shown here in full, each with the correct option and a step-by-step "Why" explanation. Sign in free with Google to practise all 90 questions with instant scoring.
Is there negative marking in the "Measuring Space: Perimeter and Area" quizzes?+
Yes — the timed quizzes use exam-grade marking: +4 for a correct answer, −1 for a wrong one and 0 for a skipped question. Note that MHT-CET and the CBSE board papers themselves carry no negative marking — our mocks for those are scored their way, not this way.
Are these important questions for Measuring Space: Perimeter and Area?+
The set is curated to the NCERT syllabus and weighted toward the question patterns that actually appear in CBSE Board exams and the JEE & NEET foundation years, across Easy, Medium and Hard — so it doubles as an "important questions" revision list for "Measuring Space: Perimeter and Area".