100 practice questions covering Perimeter and Area, organised into 2 topics. 100 questions include a written explanation. Pick a topic below, or try the samples first.
Which of these is measured in square metres?
Correct answer: A - 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.
A rectangle has area $60\ \text{cm}^2$ and perimeter $34$ cm. What are its dimensions?
Correct answer: D - $12$ 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.
Two students estimate the area of the same leaf on squared paper and get $32$ and $34$ square units. Why do the answers differ?
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.
Which of these needs a perimeter calculation rather than an area calculation?
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.
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?
Correct answer: B - $16\ \text{cm}^2$ and $24\ \text{cm}^2$
The first gives $8 \times 2 = 16\ \text{cm}^2$ and the second $6 \times 4 = 24\ \text{cm}^2$, showing that equal perimeters need not give equal areas. Option (c) reverses the order, and neither rectangle has area equal to the perimeter value.
A square's side is doubled. What happens to its area?
Correct answer: A - 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.
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