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Vidaara.orgClass 8 · Mathematics
CodeVID-M08-15-CMP-01
Composite Figures - Assignment
Chapter: Perimeter & Area
Topic: 3: Composite Figures and Mixed Problems
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.
The area of a composite figure is the ___ of its parts.
  • A.product
  • B.sum
  • C.difference
  • D.average
2.
To find a composite area, split it into:
  • A.points
  • B.known shapes
  • C.angles
  • D.lines
3.
The area of a semicircle is:
  • A.$\pi r^2$
  • B.$\tfrac12\pi r^2$
  • C.$2\pi r^2$
  • D.$\tfrac14\pi r^2$
4.
To find a remaining area, you ___ the removed region.
  • A.add
  • B.subtract
  • C.multiply
  • D.ignore
5.
When adding areas, always use the same:
  • A.shape
  • B.unit
  • C.colour
  • D.angle
Section B — Short Answer (2 marks) 4 × 2 = 8 marks
6.
A figure is made of a $6\times4$ rectangle and a $4\times3$ rectangle. Find the total area.
7.
Find the area of a $5\times5$ square with a $2\times2$ square cut out.
8.
Find the area of a semicircle of radius $7$ ($\pi=\tfrac{22}{7}$).
9.
A shape splits into areas $20$ and $15$. Find the total.
Section C — Short Answer (3 marks) 4 × 3 = 12 marks
10.
An L-shape is a $10\times6$ rectangle with a $4\times3$ rectangle removed. Find its area.
11.
A $14$ cm by $10$ cm rectangle has a semicircle of radius $7$ cm on its $14$ cm side. Find the total area ($\pi=\tfrac{22}{7}$).
12.
Find the area of a path between an outer $12\times8$ rectangle and an inner $10\times6$ rectangle.
13.
A figure is an $8\times6$ rectangle with a triangle (base $8$, height $3$) on top. Find the total area.
Section D — Long Answer (5 marks) 2 × 5 = 10 marks
14.
A room floor is an L-shape made of an $8$ m $\times$ $5$ m rectangle and a $4$ m $\times$ $3$ m rectangle. Find its area and the cost of tiling at Rs $50$ per m$^2$.
15.
A rectangular sheet $20$ cm by $14$ cm has a semicircle of radius $7$ cm cut from one short side. Find the remaining area ($\pi=\tfrac{22}{7}$).

Answer Key

Section A — Multiple Choice Questions
  1. (B) sum
  2. (B) known shapes
  3. (B) $\tfrac12\pi r^2$
  4. (B) subtract
  5. (B) unit
Section B — Short Answer (2 marks)
  1. $36$.
  2. $21$.
  3. $77$.
  4. $35$.
Section C — Short Answer (3 marks)
  1. $48$.
  2. $217$ cm$^2$.
  3. $36$.
  4. $60$.
Section D — Long Answer (5 marks)
  1. Area $52$ m$^2$; cost Rs $2600$.
  2. $203$ cm$^2$.
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