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Vidaara.orgClass 7 · Mathematics
CodeVID-M07-07-ARE-01
Area Ratio vs Side Ratio - Assignment
Chapter: Scale Drawings & Similar Figures
Topic: Area Ratio vs Side Length Ratio
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.
If the side ratio is $k$, the area ratio is:
  • A.$k$
  • B.$2k$
  • C.$k^2$
  • D.$\tfrac{k}{2}$
2.
If the side ratio is $2:3$, the area ratio is:
  • A.$2:3$
  • B.$4:9$
  • C.$8:27$
  • D.$4:6$
3.
Doubling the sides makes the area:
  • A.double
  • B.triple
  • C.$4$ times
  • D.half
4.
The perimeter ratio equals the:
  • A.area ratio
  • B.side ratio
  • C.square of side ratio
  • D.half side ratio
5.
Area scales by the ___ of the scale factor.
  • A.square
  • B.double
  • C.half
  • D.cube
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Side ratio $1:2$. Find the area ratio.
7.
Side ratio $3:1$. Find the area ratio.
8.
A side scale factor of $4$ makes the area scale by:
9.
Two similar squares have sides $2$ and $6$. Find the area ratio.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Two similar triangles have side ratio $2:5$. Find the ratio of their areas.
11.
A figure's sides are tripled. By what factor does the area increase?
12.
Two similar rectangles have areas $16$ and $64$. Find the ratio of their sides.
13.
The area ratio of two similar figures is $9:16$. Find the side ratio.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
Two similar polygons have corresponding sides in ratio $3:4$. If the area of the smaller is $27$ cm$^2$, find the area of the larger.
15.
A small square has side $5$ cm and a similar large square has side $15$ cm. Find the ratio of their perimeters and of their areas.

Answer Key

Section A — Multiple Choice Questions
  1. (C) $k^2$
  2. (B) $4:9$
  3. (C) $4$ times
  4. (B) side ratio
  5. (A) square
Section B — Short Answer (2 marks)
  1. $1:4$.
  2. $9:1$.
  3. $16$.
  4. $1:9$.
Section C — Short Answer (3 marks)
  1. $4:25$.
  2. $9$.
  3. $1:2$.
  4. $3:4$.
Section D — Long Answer (5 marks)
  1. $48$ cm$^2$.
  2. Perimeters $1:3$; areas $1:9$.
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