Mathematics

Area and Perimeter

177 Questions

Area and perimeter are fundamental concepts in mensuration and quantitative aptitude. This topic covers calculating dimensions for rectangles, squares, and various regular polygons. These practical questions frequently appear in competitive exams to evaluate spatial reasoning.

Rectangle area and breadthRegular polygon perimeterSquare propertiesFour wall surface areaError and uncertainty

Area and Perimeter Questions

Multiple choice general knowledge math & puzzles

Perimeter of a Rectangle

  1. LxB

  2. 2x(L+B)

  3. 2x(LxB)

  4. (LxB)^2
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The perimeter of a rectangle is the sum of all four sides, which equals 2 × (Length + Breadth). This is because opposite sides are equal, so you add Length + Breadth and multiply by 2. Option A (L × B) would give area, not perimeter.

Multiple choice general knowledge math & puzzles

A goat is tied to one corner of a square plot of side 12m by a rope 7m long.Find the area it can graze?

  1. 38.5 sq.m

  2. 155 sq.m

  3. 144 sq.m

  4. 19.25 sq.m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The goat can graze a quarter of a circle with radius 7m (rope length) since it's tied to a corner. Area = (1/4) × π × 7² = (1/4) × π × 49 = 38.48... ≈ 38.5 sq.m. The square plot boundary limits the goat to exactly one quadrant of the circle.

Multiple choice general knowledge math & puzzles

If the ratio of the areas of 2 squares is 2:1, then what is the ratio of the perimeters of the squares?

  1. 2:1

  2. 1:sqrt(2)

  3. 1:2

  4. sqrt(2):1
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If the areas of two squares are in ratio 2:1, then their side lengths are in ratio √2:1 (since area scales as side²). Perimeter scales linearly with side length (perimeter = 4 × side), so the perimeter ratio is also √2:1. Option A incorrectly assumes perimeter scales with area. Option B inverts the correct ratio. Option C incorrectly uses the area ratio.

Multiple choice general knowledge math & puzzles

A rectangle has the dimensions of 14 cm x 10 cm. It's length is reduced by 'x' cm and it's breadth is increased by 'x' cm to make it a square. It's area changes by -

  1. 4

  2. 144

  3. 12

  4. 2
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original area = 14 * 10 = 140. To make it a square, (14-x) = (10+x), so 2x = 4, x = 2. New dimensions are 12 * 12 = 144. The area changes from 140 to 144, a difference of 4. 144 is the new area, not the change.

Multiple choice general knowledge

A rectangle has the dimensions of 14 cm x 10 cm. It's length is reduced by 'x' cm and it's breadth is increased by 'x' cm to make it a square. It's area changes by -

  1. 4

  2. 6

  3. 5

  4. 8
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Original rectangle area = 14 x 10 = 140 sq cm. New square side = (14-x) = (10+x), so x=2 and square side = 12 cm. New square area = 12 x 12 = 144 sq cm. Area change = 144 - 140 = 4 sq cm (increase, though the question says 'changes by' which is ambiguous about direction). The calculation yields 4 as the magnitude of change.

Multiple choice

If you used the formula length + width to calculate the area of a rectangle (when it should be length x width), you would have made a _______ error.

  1. logic

  2. syntax

  3. pseudocode

  4. debugging
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

A logic error occurs when the algorithm or reasoning is wrong, even if the code is syntactically correct. Using addition instead of multiplication for area is a conceptual mistake in the problem-solving approach, not a syntax violation.

Multiple choice

Sam has two pieces of cloth. One piece is 72 inches wide and the other piece is 90 inches wide. She wants to cut both pieces into strips of equal width that are as wide as possible. How would she cut the strips?

  1. She should cut each piece to be 14 inches wide.

  2. She should cut each piece to be 16 inches wide.

  3. She should cut each piece to be 18 inches wide.

  4. She should cut each piece to be 20 inches wide.
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

 HCF of 72 and 90 = 18

Multiple choice

A rectangular field measures 480 m x 144 m and is to be paved with square tiles. The owner wants the field to be paved with SQUARE tiles with MAXIMUM covering area. Find the size of such a square tile and the total number of tiles equired to completely pave the field.

  1. 96 & 7 respectively

  2. 24 & 120 respectively

  3. 48 & 30 respectively

  4. 36 & 54 respectively

  5. 72 & 7 respectively
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Correct.

The maximum size of square tile shall be equal to the Greatest Common Divisor (GCD) of the length and breadth, i.e. 480, 144, which is 48. 

The total no. of tiles is = 480 x 144/(48 X 48) = 30.

Multiple choice

If the ratio of the areas of two squares is 9 : 25 and the sum of their areas is 306 sq. metres, then find the difference between their sides.

  1. 2 m

  2. 6 m

  3. 7 m

  4. 5 m

  5. None of these
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Let area of the 1st square = 9x sq.m and area of the 2nd square = 25x sq.m. So, 9x + 25x = 306 x = 9 Then area of the 1st square = 81 sq.metres Area of the 2nd square = 225 sq.metres So, side of the first square = 9 m and second square = 15 m. Now, differences between sides = 15 - 9 = 6.

Multiple choice

The length of a square is 5 cm. If the area of the square is equal to the difference of length and breadth of a rectangle, and the perimeter of the rectangle is 30 cm, then find the area of rectangle.

  1. 80 cm2

  2. 70 cm2

  3. 90 cm2

  4. 100 cm2

  5. None of these
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

It is given that,

Side of square = 5 cm and let the length of rectangle = l cm and breadth of rectangle = b cm.  So, l - b = area of square, = l - b = (5)2,

= l - b = 25 ---------------------(1) and,

Perimeter of rectangle = 30 cm, = 2(l + b) = 30,

= l + b = 15 --------------------(2),

After solving equation (1) and (2), we get

l = 20 cm and b = 5 cm,

So, area of rectangle = 20*5 = 100 cm2