100 practice questions on Perimeter and Area, a chapter in the NCERT Class 6 Mathematics textbook, organised into 2 topics. Every question includes a written explanation. Pick a topic below, or try the samples first.
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?
A$10$ cm by $6$ cm
B$15$ cm by $4$ cm
C$12$ cm by $5$ cm
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?
AThe leaf changed size
BThey judged the partly covered squares slightly differently
CSquared paper gives different results each time
DOne 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
easy
Which of these needs a perimeter calculation rather than an area calculation?
ABuying grass turf for a lawn
BBuying paint to cover a wall
CBuying carpet for a floor
DBuying ribbon to edge a rectangular card
Show answer and explanation
Correct answer: D - 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.
Q5
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?
ABoth $10\ \text{cm}^2$
B$24\ \text{cm}^2$ and $16\ \text{cm}^2$ in that order
C$16\ \text{cm}^2$ and $24\ \text{cm}^2$
DBoth $20\ \text{cm}^2$
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.
Q6
hard
A square's side is doubled. What happens to its area?
AIt stays the same
BIt doubles
CIt becomes four times as large
DIt 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.
Practice the full Perimeter and Area bank free
All 100 questions with timed practice, instant scoring, and explanations. Free forever.