area MCQs for UPSC Prelims

39 practice questions on area from the Perimeter and Area section of the UPSC Prelims syllabus. 39 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

12 Easy 20 Medium 7 Hard

Sample questions

Q1
easy
Which of these is measured in square metres?
  1. A The length of a corridor
  2. B The floor space of a classroom
  3. C The distance around a field
  4. D The height of a door
Show answer and explanation

Correct answer: B - The floor space of a classroom

Floor space is an area, so it is measured in square metres. Corridor length, door height and the distance round a field are all lengths, measured in plain metres.
Q2
hard
A rectangle has area $60\ \text{cm}^2$ and perimeter $34$ cm. What are its dimensions?
  1. A $10$ cm by $6$ cm
  2. B $15$ cm by $4$ cm
  3. C $12$ cm by $5$ cm
  4. D $20$ cm by $3$ cm
Show answer and explanation

Correct answer: C - $12$ cm by $5$ cm

All four pairs multiply to $60\ \text{cm}^2$, so the perimeter decides between them. Only $12$ and $5$ give $2(12 + 5) = 34$ cm. The pairs $10$ and $6$, $15$ and $4$, and $20$ and $3$ give perimeters of $32$, $38$ and $46$ cm.
Q3
medium
Two students estimate the area of the same leaf on squared paper and get $32$ and $34$ square units. Why do the answers differ?
  1. A The leaf changed size
  2. B They judged the partly covered squares slightly differently
  3. C Squared paper gives different results each time
  4. D One of them must have counted wrongly
Show answer and explanation

Correct answer: B - They judged the partly covered squares slightly differently

Deciding whether a partly covered square counts is a judgement, so small differences between careful students are expected. Neither need have miscounted, the leaf did not change, and the paper itself is consistent.
Q4
medium
Two rectangles both have perimeter $20$ cm. One is $8$ cm by $2$ cm and the other $6$ cm by $4$ cm. What are their areas?
  1. A Both $10\ \text{cm}^2$
  2. B $24\ \text{cm}^2$ and $16\ \text{cm}^2$ in that order
  3. C $16\ \text{cm}^2$ and $24\ \text{cm}^2$
  4. D Both $20\ \text{cm}^2$
Show answer and explanation

Correct answer: C - $16\ \text{cm}^2$ and $24\ \text{cm}^2$

The $8$ cm by $2$ cm rectangle has area $8 \times 2 = 16\ \text{cm}^2$ and the $6$ cm by $4$ cm one has $6 \times 4 = 24\ \text{cm}^2$, so equal perimeters need not give equal areas. Listing $24\ \text{cm}^2$ before $16\ \text{cm}^2$ swaps the two rectangles. Neither area equals the perimeter value, so $10\ \text{cm}^2$ and $20\ \text{cm}^2$ are both wrong.
Q5
hard
A square's side is doubled. What happens to its area?
  1. A It stays the same
  2. B It doubles
  3. C It becomes four times as large
  4. D It becomes eight times as large
Show answer and explanation

Correct answer: C - It becomes four times as large

If the side goes from $a$ to $2a$, the area goes from $a \times a$ to $2a \times 2a = 4 \times a \times a$, so it quadruples. The perimeter doubles, but the area grows by the square of the factor.
Q6
medium
A room floor is $6$ m long and $5$ m wide. How many square metres of tiles are needed to cover it?
  1. A $11\ \text{m}^2$
  2. B $22\ \text{m}^2$
  3. C $30\ \text{m}^2$
  4. D $60\ \text{m}^2$
Show answer and explanation

Correct answer: C - $30\ \text{m}^2$

The area is $6 \times 5 = 30\ \text{m}^2$ of tiles. Answering $22\ \text{m}^2$ gives the perimeter, $11\ \text{m}^2$ adds the sides, and $60\ \text{m}^2$ doubles the area.
Q7
medium
A rectangle has area $96\ \text{cm}^2$ and length $16$ cm. What is its breadth?
  1. A $6$ cm
  2. B $8$ cm
  3. C $12$ cm
  4. D $80$ cm
Show answer and explanation

Correct answer: A - $6$ cm

Dividing gives $96 \div 16 = 6$ cm. Answering $80$ cm subtracts, $12$ cm would give an area of $192\ \text{cm}^2$, and $8$ cm would give $128\ \text{cm}^2$.
Q8
medium
A shape on squared paper covers $9$ full squares and $10$ half squares. What is its area?
  1. A $24$ square units
  2. B $9$ square units
  3. C $14$ square units
  4. D $19$ square units
Show answer and explanation

Correct answer: C - $14$ square units

The ten half squares make $5$ full squares, so the total is $9 + 5 = 14$ square units. Answering $19$ counts each half as a whole, $9$ ignores the halves, and $24$ over-counts them.

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