Are these practice questions for Measuring Space: Perimeter and Area based on the CBSE pattern?

Yes. Every practice question is modeled on the CBSE Class 9 Mathematics exam pattern — including MCQs, assertion-reason questions, and short-answer formats that frequently appear in CBSE papers.

Are the practice questions for Measuring Space: Perimeter and Area free?

Yes. Every chapter includes free practice questions for Class 9 students to get you started.

What types of questions are included?

The practice set for Measuring Space: Perimeter and Area mainly includes MCQs and CBSE-style short-answer questions, with instant feedback on each answer. For full-length textbook practice, use the NCERT Solutions page.

Are the practice questions suitable for board exam preparation?

Yes. The questions test the same concepts and depth that CBSE asks in board exams. After finishing, also solve the NCERT and NCERT Exemplar exercises for Measuring Space: Perimeter and Area for full coverage.

How many practice questions are there for Measuring Space: Perimeter and Area?

The number scales with chapter length and concept density. Each chapter typically has 15-50 practice questions across MCQ and short-answer formats.

Measuring Space: Perimeter and Area Class 9 Mathematics Practice Questions with Answers

easy

A student claims

\pi = \frac{22}{7}

. Critique this mathematical statement.

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easy

State Heron's formula for the area of a triangle and define each variable used.

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easy

Two paths connect points P and Q. Path 1 is a large semicircle with diameter PQ. Path 2 consists of two smaller, equal semicircles whose diameters are PX and XQ, where X is the midpoint of PQ. A person claims Path 1 is shorter because it is a single, direct curve. Evaluate this claim mathematically.

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easy

Explain why athletes in outer lanes start ahead of athletes in inner lanes in a

4 \times 100

m relay race.

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easy

State the formula for the area of a triangle with base

b

and height

h

.

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easy

What is an irrational number? Give one example from the text.

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easy

State the formula for the area of a sector of a circle and explain the meaning of each variable.

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easy

Justify why, for an athletics race that covers one or more curves (like a 400m race), runners in outer lanes are given a staggered start.

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easy

Identify the constant ratio that the number

\pi

represents in any circle.

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easy

Define the term 'perimeter' as it applies to a two-dimensional shape.

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easy

Calculate the perimeter of a sector of a circle with a radius of 14 cm and a central angle of

90^\circ

. (Use

\pi = \frac{22}{7}

)

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easy

The area of a rhombus is 144 cm² and the length of one of its diagonals is 18 cm. Calculate the length of the other diagonal.

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easy

State the formula for the circumference of a circle in terms of its radius,

r

.

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medium

A copper wire, when bent in the form of a square, encloses an area of 121 cm². If the same wire is bent into the shape of a circle, calculate the area of the circle. (Use

\pi = \frac{22}{7}

)

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medium

Describe the method used by Archimedes to approximate the value of

\pi

. Explain how his use of an inscribed hexagon showed that

\pi > 3

.

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medium

Critique the following statement: 'The area of any quadrilateral can be determined if only the lengths of its four sides are known.' Use a diagram to justify your position.

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medium

Summarize the major contribution of Mādhava of Sangamagrāma to the calculation of

\pi

. What was mathematically significant about his formula compared to earlier approximations?

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medium

Justify the theorem: 'A median of a triangle divides it into two triangles of equal area.'

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medium

Derive the formula for the area of an equilateral triangle with side 'a' as

\frac{\sqrt{3}}{4}a^2

using two different methods:

The standard formula $\frac{1}{2} \times \text{base} \times \text{height}$ combined with the Baudhāyana-Pythagoras theorem.
Heron's formula. Justify that both methods yield the same result.

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medium

A bicycle wheel has a diameter of 56 cm. Calculate the distance covered by the bicycle after the wheel completes 50 revolutions. (Use

\pi = \frac{22}{7}

)

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medium

The adjacent sides of a parallelogram are 15 cm and 10 cm. If the distance between the longer sides (15 cm) is 8 cm, calculate the distance between the shorter sides (10 cm).

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medium

The perimeter of an equilateral triangle is 48 cm. Calculate its area.

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medium

Two triangles are on the same base of length 10 cm. The ratio of their heights is 4:5. Analyze and find the ratio of their areas.

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medium

Design a method to find the area of an irregular pentagon using only a ruler, a set square, and the formula for the area of a triangle. Justify the steps in your method.

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medium

Explain why a median of a triangle divides it into two triangles of equal area.

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medium

The minute hand of a clock is 14 cm long. Calculate the area swept by the minute hand in 15 minutes. (Use

\pi = \frac{22}{7}

)

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medium

List two different fractional approximations for

\pi

mentioned in the text and name the mathematician or civilization associated with each.

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medium

A farmer has a field in the shape of a quadrilateral PQRS. The sides are PQ = 21 m, QR = 20 m, RS = 13 m, SP = 34 m, and the diagonal QS = 25 m. Calculate the area of the field.

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medium

A triangular field has sides 91 m, 98 m, and 105 m. Calculate its area using Heron's formula.

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medium

Describe the difference between the 'circumcircle' and the 'incircle' of a triangle.

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medium

A triangular park has sides 50 m, 65 m, and 65 m. A gardener claims it is more efficient to calculate its area using the formula

\frac{1}{2} \times \text{base} \times \text{height}

than using Heron's formula. Evaluate this claim by performing both calculations and justifying which method is more straightforward for this specific triangle.

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medium

A park is in the shape of a rectangle with semicircular ends. The rectangular portion has a length of 100 m and a width of 56 m. Calculate the perimeter of the park and the total area of the park. (Use

\pi = \frac{22}{7}

)

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medium

In

\triangle ABC

, D is the midpoint of side BC. The area of

\triangle ABD

is 24 cm². Analyze the figure to find the area of

\triangle ABC

. Further, if P is the midpoint of the median AD, what is the area of

\triangle BPD

?

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hard

Formulate a general principle connecting the area of a regular n-sided polygon to its perimeter and the radius of its inscribed circle (apothem).

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hard

If the mid-points of the sides of any quadrilateral are joined in order, the resulting figure is a parallelogram. Justify that the area of this parallelogram is exactly half the area of the original quadrilateral.

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hard

Explain why knowing only the lengths of the four sides is not sufficient to determine the area of a general quadrilateral. Use the example of a rhombus to support your explanation.

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hard

In a circle, a chord AB is drawn. Prove that for any point C on the major arc AB, the area of

\triangle ABC

is maximized when the triangle is isosceles (i.e., when C is the midpoint of the arc AB). Justify your reasoning.

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hard

Explain the key difference between Heron's formula and Brahmagupta's formula. Describe how Brahmagupta's formula can be considered a generalization of Heron's formula.

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hard

Create a composite shape made of one rectangle and two different semicircles, such that its total perimeter is exactly

100

cm. Provide a diagram with labeled dimensions and justify your calculations. (Use

\pi = \frac{22}{7}

)

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hard

A square and an equilateral triangle have the same perimeter. Formulate the ratio of the area of the square to the area of the equilateral triangle.

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hard

The circumference of a circular park is 88 m. A path of width 3.5 m is laid around the outside of the park. Calculate the area of the path. (Use

\pi = \frac{22}{7}

)

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hard

You are tasked with designing a 200m running track for a school. The track must consist of two straight sections and two semicircular ends. The total length of the inner lane must be exactly 200m. The width of each lane is 1.22 m.

a) Propose one possible set of dimensions (length of straight, radius of curve) for the track. b) Create a formula to calculate the stagger required for the runner in Lane 2 for a 200m race (one full lap). Justify your formula.

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hard

Calculate the area of an isosceles trapezium with parallel sides of 42 cm and 20 cm, and non-parallel sides of 13 cm each.

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hard

A square handkerchief of side 40 cm has four circular quadrants, each of radius 7 cm, cut from its four corners. The boundary of the remaining part is then stitched with a lace. Calculate the area of the remaining part and the length of the lace required. (Use

\pi = \frac{22}{7}

)

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hard

A student asserts that since

\pi

is an irrational number, it is impossible to construct a square that has the exact same area as a given circle using only a compass and straightedge. Evaluate this assertion.

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Measuring Space: Perimeter and AreaClass 9 Mathematics Practice Questions