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Class 9 Maths: Measuring Space, Perimeter and Area, 8 practice questions with answers

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These are 8 practice questions on Chapter 6, Measuring Space: Perimeter and Area, of the new NCERT Class 9 Maths textbook, Ganita Manjari, Part I (First Edition, April 2026). Each has a worked answer, the units, and the textbook page it comes from. They cover the perimeter of a rectangle, the circumference and area of a circle, a rolling wheel, and Heron's formula for a triangle and for a four-sided figure. Try each one on paper before you open the answer. The surface area and volume of a cuboid and a cylinder are in the Class 9 Surface Area and Volume questions.

These questions are our own, drafted with AI help. Every number was re-computed by a test script, but no practising teacher has reviewed them yet. If you find a mistake, please tell us.

What the chapter says you need

Facts from the NCERT textbook (Ganita Manjari: Mathematics, Textbook for Grade 9, Part I, Chapter 6, printed pages 118 to 154):

Perimeter and the circle

Question 1. A rectangular field is 40 m long and 25 m wide. What is its perimeter in m?

Answer: 130 m. Perimeter = 2 × (length + width) = 2 × 65 = 130 m. (Page 119.)

Question 2. Meera runs once around a circular track of radius 35 m. Ravi runs once around a square track of side 55 m. Using 22/7 for π, who runs farther?

Answer: they run the same distance, 220 m. One round of the circle is its circumference: 2πr = 2 × 22/7 × 35 = 220 m. One round of the square is its perimeter: 4 × 55 = 220 m. So neither runs farther. (Circumference of a circle and the approximation 22/7, pages 124 and 125; perimeter of a square, page 119.)

Question 3. A circle has a radius of 14 cm. Using 22/7 for π, what is its area in square cm?

Answer: 616 cm². Area = πr² = 22/7 × 14 × 14 = 22 × 2 × 14 = 616 square cm. (The true value is about 615.75 cm²; pages 124 and 145.)

Question 4. A wheel of radius 35 cm makes 10 full turns. Using 22/7 for π, how far does it roll, in cm?

Answer: 2,200 cm. One turn = the circumference = 2 × 22/7 × 35 = 220 cm. Ten turns = 2,200 cm. (The true value is about 2,199.1 cm. Circumference, page 125; the textbook's own tyre exercise, which asks how far a car travels for one revolution of the tyre, is Exercise Set 6.1, question 6, page 130.)

Heron's formula

Heron's formula: area = √(s(s − a)(s − b)(s − c)), where s is half the perimeter (page 134).

Question 5. A triangle has sides 5 cm, 5 cm and 6 cm. Using Heron's formula, what is its area in square cm?

Answer: 12 cm². s = (5 + 5 + 6) ÷ 2 = 8; area = √(8 × 3 × 3 × 2) = √144 = 12 square cm. (Page 134; the textbook treats the isosceles case on page 135.)

Question 6. Use Heron's formula to find the area of a triangle with sides 13 cm, 14 cm and 15 cm, in square cm.

Answer: 84 cm². Semi-perimeter s = (13 + 14 + 15) ÷ 2 = 21. Heron's formula multiplies s by s − 13, s − 14 and s − 15, then takes the square root: √(21 × 8 × 7 × 6) = √7056 = 84 square cm. (Page 134.)

Question 7. A triangle has sides 7 cm, 15 cm and 20 cm. Find its area in square cm using Heron's formula. (This question is not in the practice set.)

Answer: 42 cm². s = (7 + 15 + 20) ÷ 2 = 21. Area = √(21 × 14 × 6 × 1) = √1764 = 42 square cm. (Page 134.)

Question 8. In the quadrilateral ABCD, AB = 3 cm, BC = 4 cm, CD = 5 cm, DA = 6 cm and the diagonal AC = 5 cm; the diagonal AC lies inside ABCD. Using Heron's formula for the two triangles, find the area of ABCD, in square cm.

Answer: 18 cm². The diagonal AC splits ABCD into triangles ABC (3, 4, 5) and ACD (5, 5, 6). Triangle ABC: s = 6, area = √(6 × 3 × 2 × 1) = 6. Triangle ACD: s = 8, area = √(8 × 3 × 3 × 2) = √144 = 12. Area of ABCD = 6 + 12 = 18 square cm. (Heron's formula, page 134; a four-sided figure needs a diagonal besides its four sides, page 137.)

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Sources

All opened and read on 21 October 2026. Page numbers are the printed page numbers of the textbook; printed page = PDF page + 117.

The formulas and definitions are from the textbook pages above. The questions, worked answers and checks are our own, and every number was re-computed by script. This guide is general information; follow your teacher and the textbook.