Vidaara.orgClass 9 · Mathematics
CodeVID-M9-09-CT
Areas of Parallelograms and Triangles — Full Chapter Test
Name: ____________________
Roll No.: __________
Date: ____________
General Instructions
- This is a full-length test covering the whole chapter — every topic is included.
- All questions are compulsory.
- Section A carries 1 mark each, Section B 2 marks, Section C 3 marks and Section D 5 marks.
- Show all working for Sections B, C and D. Only final answers are given at the end — for full solutions, raise your doubts with your teacher.
Section A — Multiple Choice Questions
5 × 1 = 5 marks
1.
Area is measured in:
- A.units
- B.square units
- C.cubic units
- D.degrees
2.
Area of a parallelogram $=$
- A.base $\times$ height
- B.$\tfrac12$ base $\times$ height
- C.side$^2$
- D.base $+$ height
3.
Parallelograms on the same base/parallels are equal in:
- A.perimeter
- B.area
- C.angle
- D.diagonal
4.
Congruent figures have:
- A.equal areas
- B.unequal areas
- C.no area
- D.equal angles only
5.
Area of a triangle $=$
- A.base $\times$ height
- B.$\tfrac12$ base $\times$ height
- C.side$^2$
- D.$2bh$
Section B — Short Answer (2 marks)
4 × 2 = 8 marks
6.
Do congruent figures have equal area?
7.
Find the area of a parallelogram with base $8$ and height $5$.
8.
Two triangles on the same base/parallels have areas in what ratio?
9.
If two rectangles have area $12$, are they necessarily congruent?
Section C — Short Answer (3 marks)
4 × 3 = 12 marks
10.
A figure is split into a $6$ and an $8$ square-unit part. Find its total area.
11.
A triangle has base $12$ cm and area $54$ cm$^2$. Find its height.
12.
Triangles $ABC$ and $DBC$ are on the same base $BC$ between the same parallels; if area $ABC=25$, find area $DBC$.
13.
Must equal-area figures be congruent?
Section D — Long Answer (5 marks)
2 × 5 = 10 marks
14.
A rectangular field $40$ m by $30$ m has an internal path of area $200$ m$^2$. Find the area of the field excluding the path.
15.
A parallelogram and a triangle are on the same base and between the same parallels. If the parallelogram's area is $48$ cm$^2$, find the triangle's area and explain the relationship.
Answer Key
Section A — Multiple Choice Questions
- (B) square units
- (A) base $\times$ height
- (B) area
- (A) equal areas
- (B) $\tfrac12$ base $\times$ height
Section B — Short Answer (2 marks)
- Yes.
- $40$.
- $1:1$.
- No.
Section C — Short Answer (3 marks)
- $14$.
- $9$ cm.
- $25$.
- No.
Section D — Long Answer (5 marks)
- $1000$ m$^2$.
- $24$ cm$^2$ (the triangle is half the parallelogram).
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