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.
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.
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.
A room floor is $6$ m long and $5$ m wide. How many square metres of tiles are needed to cover it?
Correct answer: D - $30\ \text{m}^2$
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.
A rectangle has area $96\ \text{cm}^2$ and length $16$ cm. What is its breadth?
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 $128\ \text{cm}^2$.
A shape on squared paper covers $9$ full squares and $10$ half squares. What is its area?
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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