Chapter 9 · Class 9 CBSE · Worksheet

Areas of Parallelograms & Triangles Worksheet — Class 9 CBSE Maths

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Sample Questions — Areas of Parallelograms & Triangles

Here are 8 sample questions from this worksheet. Download the full PDF for all 30 questions.

Q1.For two planar figures to be considered 'between the same parallels', what is the essential condition they must satisfy?

A.Their bases must lie on one parallel line, and their vertices opposite to the base must lie on the other parallel line.
B.They must have at least one common side.
C.Their areas must be equal.
D.They must be congruent.

Difficulty: Easy

Q2.In a figure, parallelogram ABCD and triangle EBC are drawn such that point E lies on the side AD. For these two figures to be on the same base and between the same parallels, which condition is necessary?

A.E must be the midpoint of AD.
B.The line AD must be parallel to the line BC.
C.The line AB must be parallel to the line CD.
D.Area(ABCD) must be equal to Area(EBC).

Difficulty: Easy

Q3.Parallelogram PQRS and parallelogram MNRS are on the same base SR and between the same parallels SR and PM. If Area(PQRS) = 45 cm², what is Area(MNRS)?

A.90 cm²
B.45 cm²
C.22.5 cm²
D.Cannot be determined without side lengths.

Difficulty: Easy

Q4.Which of the following conditions is *not necessarily true* for two triangles on the same base and between the same parallels?

A.Their heights corresponding to the common base are equal.
B.Their areas are equal.
C.They have the same perimeter.
D.Their vertices opposite to the common base lie on the same parallel line.

Difficulty: Easy

Q5.A triangle and a parallelogram are on the same base and between the same parallels. If the area of the parallelogram is 60 cm², what is the area of the triangle?

A.30 cm²
B.60 cm²
C.120 cm²
D.45 cm²

Difficulty: Easy

Q6.Ravi claims that if two triangles have the same base, their areas must be equal. Which of the following statements *best explains* why Ravi's claim is incorrect?

A.Triangles on the same base always have different areas.
B.Their areas are equal only if they are congruent.
C.Their areas are equal only if they are right-angled triangles.
D.Their areas are equal only if their heights corresponding to that base are also equal.

Difficulty: Easy

Q7.If two triangles have the same base and equal areas, then their corresponding vertices opposite to the common base must lie on a line __________ to the base.

A.perpendicular
B.intersecting
C.parallel
D.oblique

Difficulty: Easy

Q8.In ΔPQR, if PS is a median to side QR, and Area(ΔPQS) = 35 cm², what is Area(ΔPQR)?

A.70 cm²
B.35 cm²
C.17.5 cm²
D.Cannot be determined.

Difficulty: Easy

Answer Key — Sample Questions+
Q1:A
Q2:B
Q3:B
Q4:C
Q5:A
Q6:D
Q7:C
Q8:A

Download the full PDF for all 30 answers with step-by-step solutions.

About This Worksheet

TopicAreas of Parallelograms & Triangles
BoardCBSE
Class9
Total Questions30 (10 Easy + 10 Medium + 10 Hard)
Answer KeyIncluded
PriceFree

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Frequently Asked Questions

Where can I download a free Areas of Parallelograms & Triangles worksheet for Class 9?+
You can download a free Areas of Parallelograms & Triangles PDF worksheet for Class 9 CBSE right here on SparkEd. The worksheet includes 30 questions at easy, medium, and hard levels with a complete answer key.
How many questions are in the Areas of Parallelograms & Triangles worksheet?+
Each SparkEd worksheet for Areas of Parallelograms & Triangles contains 30 questions — 10 easy, 10 medium, and 10 hard. A fresh set is generated daily so you never repeat the same sheet.
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Yes. Every SparkEd worksheet comes with a separate answer key so students can self-check their work after completing the sheet.

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