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Vidaara.orgClass 7 · Mathematics
CodeVID-M7-07-CT
Scale Drawings & Similar Figures — Full Chapter Test
Chapter: Scale Drawings & Similar Figures
Topic: Complete chapter — all topics
Maximum Marks: 35
Time: 75 minutes
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.
Similar polygons have the same shape but not necessarily the same:
  • A.angles
  • B.size
  • C.sides
  • D.name
2.
If the side ratio is $k$, the area ratio is:
  • A.$k$
  • B.$2k$
  • C.$k^2$
  • D.$\tfrac{k}{2}$
3.
Corresponding angles of similar polygons are:
  • A.equal
  • B.supplementary
  • C.different
  • D.zero
4.
If the side ratio is $2:3$, the area ratio is:
  • A.$2:3$
  • B.$4:9$
  • C.$8:27$
  • D.$4:6$
5.
Corresponding sides of similar polygons are:
  • A.equal
  • B.proportional
  • C.perpendicular
  • D.unrelated
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
Do similar figures have equal corresponding angles?
7.
Side ratio $1:2$. Find the area ratio.
8.
Are the corresponding sides of similar figures proportional?
9.
Side ratio $3:1$. Find the area ratio.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
Two similar rectangles: the first is $4\times6$ and the second has width $8$. Find its length.
11.
Two similar triangles have side ratio $2:5$. Find the ratio of their areas.
12.
A triangle with sides $3,4,5$ is similar to one with shortest side $6$. Find the other two sides.
13.
A figure's sides are tripled. By what factor does the area increase?
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
$\triangle ABC\sim\triangle DEF$ with $AB=6$, $BC=8$, $AC=10$ and $DE=9$. Find the scale factor and the lengths $EF$ and $DF$.
15.
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.

Answer Key

Section A — Multiple Choice Questions
  1. (B) size
  2. (C) $k^2$
  3. (A) equal
  4. (B) $4:9$
  5. (B) proportional
Section B — Short Answer (2 marks)
  1. Yes.
  2. $1:4$.
  3. Yes.
  4. $9:1$.
Section C — Short Answer (3 marks)
  1. $12$.
  2. $4:25$.
  3. $8$ and $10$.
  4. $9$.
Section D — Long Answer (5 marks)
  1. Scale factor $1.5$; $EF=12$, $DF=15$.
  2. $48$ cm$^2$.
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