perimeter MCQs for UPSC Prelims

37 practice questions on perimeter from the Perimeter and Area section of the UPSC Prelims syllabus. 37 come with a written explanation. Try the sample set below - the answer stays hidden until you ask for it.

13 Easy 18 Medium 6 Hard

Sample questions

Q1
easy

Which of these needs a perimeter calculation rather than an area calculation?

  1. A Buying carpet for a floor
  2. B Buying ribbon to edge a rectangular card
  3. C Buying paint to cover a wall
  4. D Buying grass turf for a lawn
Show answer and explanation

Correct answer: B - Buying ribbon to edge a rectangular card

Edging runs along the boundary, so ribbon length is the perimeter. Paint, carpet and turf all cover surfaces, which is a question of area.

Q2
hard

A square and an equilateral triangle have the same perimeter. If the square's side is $6$ cm, what is the triangle's side?

  1. A $6$ cm
  2. B $8$ cm
  3. C $12$ cm
  4. D $4$ cm
Show answer and explanation

Correct answer: B - $8$ cm

The square's perimeter is $4 \times 6 = 24$ cm, so each side of the triangle is $24 \div 3 = 8$ cm. Answering $6$ cm copies the square's side, $12$ cm halves the perimeter, and $4$ cm divides by $6$.

Q3
easy

A square handkerchief of side $25$ cm is edged with lace. How much lace is needed?

  1. A $50$ cm
  2. B $75$ cm
  3. C $100$ cm
  4. D $625$ cm
Show answer and explanation

Correct answer: C - $100$ cm

The lace runs around the perimeter, which is $4 \times 25 = 100$ cm. Answering $625$ cm gives the area, $50$ cm covers two sides, and $75$ cm covers three.

Q4
medium

A rectangular field is $45$ m long and $30$ m wide. How much wire is needed to fence it once round?

  1. A $1350$ m
  2. B $75$ m
  3. C $90$ m
  4. D $150$ m
Show answer and explanation

Correct answer: D - $150$ m

The perimeter is $2(45 + 30) = 150$ m of wire. Answering $75$ m adds the sides once, $1350$ m gives the area, and $90$ m doubles only the length.

Q5
easy

How is the perimeter of an irregular polygon found?

  1. A By multiplying length and breadth
  2. B By multiplying the longest side by the number of sides
  3. C By counting its corners
  4. D By adding the lengths of all its sides
Show answer and explanation

Correct answer: D - By adding the lengths of all its sides

With unequal sides there is no shortcut, so every side must be added. Multiplying the longest side would overstate the total, length times breadth gives an area, and corners give no length.

Q6
easy

In which unit is perimeter measured?

  1. A No unit is needed
  2. B Units of length, such as centimetres
  3. C Square units, such as square centimetres
  4. D Cubic units
Show answer and explanation

Correct answer: B - Units of length, such as centimetres

Perimeter is a distance, so it is measured in units of length such as centimetres or metres. Square units measure area, cubic units measure volume, and every measurement needs a unit.

Q7
easy

What is the formula for the perimeter of a rectangle of length $l$ and breadth $b$?

  1. A $l \times b$
  2. B $4l$
  3. C $l + b$
  4. D $2(l + b)$
Show answer and explanation

Correct answer: D - $2(l + b)$

A rectangle has two lengths and two breadths, so the perimeter is $l + b + l + b = 2(l + b)$. The product $l \times b$ gives the area, $l + b$ counts only one of each side, and $4l$ would apply to a square of side $l$.

Q8
medium

A rectangle has perimeter $50$ cm and breadth $10$ cm. What is its length?

  1. A $20$ cm
  2. B $25$ cm
  3. C $40$ cm
  4. D $15$ cm
Show answer and explanation

Correct answer: D - $15$ cm

From $2(l + b) = 50$ we get $l + b = 25$, so $l = 25 - 10 = 15$ cm. Answering $40$ cm subtracts from the whole perimeter, $25$ cm forgets to subtract the breadth, and $20$ cm does not fit the perimeter.

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