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Vidaara.orgClass 9 · Mathematics
CodeVID-M09-09-ATP-01
Area of Triangles & Parallelograms - Assignment
Chapter: Areas of Parallelograms and Triangles
Topic: Area of Triangles and Parallelograms
Maximum Marks: 35
Time: 75 minutes
Name: ____________________ Roll No.: __________ Date: ____________

General Instructions

  • 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 of a parallelogram $=$
  • A.base $\times$ height
  • B.$\tfrac12$ base $\times$ height
  • C.side$^2$
  • D.base $+$ height
2.
Area of a triangle $=$
  • A.base $\times$ height
  • B.$\tfrac12$ base $\times$ height
  • C.side$^2$
  • D.$2bh$
3.
A triangle on the same base/parallels as a parallelogram has area:
  • A.equal
  • B.half
  • C.twice
  • D.a quarter
4.
Area of a parallelogram, base $5$, height $4$:
  • A.$9$
  • B.$20$
  • C.$40$
  • D.$10$
5.
Area of a triangle, base $6$, height $8$:
  • A.$48$
  • B.$24$
  • C.$14$
  • D.$28$
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Find the area of a parallelogram with base $8$ and height $5$.
7.
Find the area of a triangle with base $10$ and height $6$.
8.
A parallelogram and a triangle are on the same base/parallels. Find the ratio of their areas.
9.
Find the height of a parallelogram of area $48$ and base $6$.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
A triangle has base $12$ cm and area $54$ cm$^2$. Find its height.
11.
Two parallelograms on the same base $10$ between the same parallels have height $5$. Find each area.
12.
Find the area of a parallelogram with base $7$ cm and height $4$ cm.
13.
A triangle and a parallelogram share a base and lie between the same parallels; the parallelogram area is $60$. Find the triangle's area.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
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.
15.
A triangle has area $90$ cm$^2$ and base $15$ cm. Find its height; then find the new area if the base is doubled and the height halved.

Answer Key

Section A — Multiple Choice Questions
  1. (A) base $\times$ height
  2. (B) $\tfrac12$ base $\times$ height
  3. (B) half
  4. (B) $20$
  5. (B) $24$
Section B — Short Answer (2 marks)
  1. $40$.
  2. $30$.
  3. $2:1$.
  4. $8$.
Section C — Short Answer (3 marks)
  1. $9$ cm.
  2. $50$ each.
  3. $28$ cm$^2$.
  4. $30$.
Section D — Long Answer (5 marks)
  1. $24$ cm$^2$ (the triangle is half the parallelogram).
  2. Height $12$ cm; new area $90$ cm$^2$ (unchanged).
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