A rectangle is 12 cm long and 8 cm broad. What is its area?

96 cm². Area = l b = 12 8 = 96 cm².

What is the area of a triangle with base 10 cm and height 6 cm?

30 cm². Area = 12 10 6 = 30 cm².

The area of a square is 144 cm². What is its perimeter?

48 cm. Side = 144 = 12 cm, so the perimeter is 4 12 = 48 cm.

If a rectangle's length is increased by 20% and its breadth decreased by 20%, how does the area change?

4% decrease. New area = 1.2 0.8 = 0.96 times the original — a 4% decrease.

A rectangular lawn 30 m by 20 m has a path 2 m wide running all around it on the outside. What is the area of the path?

216 m². The outer rectangle is 34 24 = 816 m² and the lawn is 30 20 = 600 m². The path is 816 - 600 = 216 m².

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Quantitative Aptitude · Geometry & Mensuration

Area — Questions & Answers

Area questions apply the standard plane formulas and then reason about changes: a path of uniform width around a lawn, a percentage change in a side, or the ratio of areas of similar figures.

5 solved questions
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Key formulas included

Key formulas

Rectangle: $l \times b$ ; square: $a^2$ ; triangle: $\tfrac{1}{2}\,b\,h$
Circle: area $\pi r^2$ , circumference $2\pi r$
Equilateral triangle of side $a$ : area $\dfrac{\sqrt{3}}{4}a^2$

5 solved Area questions

Try each question first — tap an option to check your answer, or open Learn step by step for a guided walkthrough.

01
A rectangle is 12 cm long and 8 cm broad. What is its area?
4 steps · reveal one at a time
1. Step 1: Understand the Question
  We need to find the area of a rectangle. We are given its length as $12$ cm and its breadth as $8$ cm. These are the key facts.
2. Step 2: Recall the Formula
  The formula for the area of a rectangle is length multiplied by breadth. In mathematical terms, this is $A = l \times b$ , where $A$ is the area, $l$ is the length, and $b$ is the breadth.
3. Step 3: Calculate the Area
  Now, substitute the given values into the formula: $A = 12 \text{ cm} \times 8 \text{ cm}$ . Perform the multiplication to find the area.
4. Step 4: The answer
  So the answer is (B) 96 cm². The product of $12 \times 8$ is $96$ , and the units are square centimeters.
02
What is the area of a triangle with base 10 cm and height 6 cm?
4 steps · reveal one at a time
1. Step 1: Understand the Question
  We need to find the area of a triangle. We are given the base as $10$ cm and the height as $6$ cm. These are the two key measurements needed.
2. Step 2: Recall the Formula
  The standard formula for the area of a triangle is half times its base times its height. This can be written as Area $= \frac{1}{2} \times \text{base} \times \text{height}$ .
3. Step 3: Calculate the Area
  Now, substitute the given values into the formula. The base is $10$ cm and the height is $6$ cm. So, the calculation becomes Area $= \frac{1}{2} \times 10 \times 6$ .
4. Step 4: The answer
  Perform the multiplication: Area $= \frac{1}{2} \times 60 = 30$ cm $^2$ . So the answer is (D) 30 cm². This is the correct area for the triangle.
03
The area of a square is 144 cm². What is its perimeter?
4 steps · reveal one at a time
1. Step 1: Understand the Area
  The area of a square is found by multiplying its side length by itself (side squared). We are given that the area is $144 \text{ cm}^2$ .
2. Step 2: Calculate Side Length
  To find the side length of the square, we need to take the square root of its area. So, the side length $s = \sqrt{144 \text{ cm}^2} = 12 \text{ cm}$ .
3. Step 3: Find the Perimeter
  The perimeter of a square is the total length of all its four sides. Since all sides are equal, you multiply the side length by $4$ . So, the perimeter is $4 \times 12 \text{ cm}$ .
4. Step 4: The answer
  So the answer is (B) 48 cm. The perimeter is $4 \times 12 = 48 \text{ cm}$ . This matches option (B).
04
If a rectangle's length is increased by 20% and its breadth decreased by 20%, how does the area change?
5 steps · reveal one at a time
1. Step 1: Original Area
  Let the original length of the rectangle be $L$ and its original breadth be $B$ . The original area, $A$ , is calculated as $A = L \times B$ . This is the baseline we will compare against.
2. Step 2: Calculate New Dimensions
  The length is increased by 20%, so the new length $L'$ is $L + 0.20L = 1.20L$ . The breadth is decreased by 20%, making the new breadth $B'$ equal to $B - 0.20B = 0.80B$ .
3. Step 3: Find New Area
  Now, calculate the new area, $A'$ , using the new length and breadth. So, $A' = L' \times B' = (1.20L) \times (0.80B)$ . We can multiply the numerical factors together.
4. Step 4: Compare Areas
  Multiplying the factors, we get $A' = (1.20 \times 0.80) \times (L \times B) = 0.96 \times (L \times B)$ . Since $L \times B$ is the original area $A$ , the new area $A' = 0.96A$ .
5. Step 5: The answer
  So the answer is (C) 4% decrease. The new area is $0.96$ times the original area, which means it is $1 - 0.96 = 0.04$ or 4% less than the original area.
05
A rectangular lawn 30 m by 20 m has a path 2 m wide running all around it on the outside. What is the area of the path?
5 steps · reveal one at a time
1. Step 1: Identify Dimensions
  First, let's note the dimensions of the rectangular lawn. Its length is $30 \text{ m}$ and its width is $20 \text{ m}$ . The path is $2 \text{ m}$ wide and runs around the outside of the lawn.
2. Step 2: Calculate Lawn Area
  The area of the lawn itself can be calculated using the formula for the area of a rectangle: length $\times$ width. So, the area of the lawn is $30 \text{ m} \times 20 \text{ m} = 600 \text{ m}^2$ .
3. Step 3: Find Outer Dimensions
  Since the path is $2 \text{ m}$ wide on all sides, the total length of the lawn plus path will be $30 + 2 + 2 = 34 \text{ m}$ . The total width will be $20 + 2 + 2 = 24 \text{ m}$ .
4. Step 4: Calculate Outer Area
  Now, calculate the total area of the lawn including the path. This forms a larger rectangle with dimensions $34 \text{ m}$ by $24 \text{ m}$ . Its area is $34 \text{ m} \times 24 \text{ m} = 816 \text{ m}^2$ .
5. Step 5: The answer
  So the answer is (C) 216 m². To find the area of the path, subtract the lawn's area from the total area: $816 \text{ m}^2 - 600 \text{ m}^2 = 216 \text{ m}^2$ .

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