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 physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The length and breadth of a rectangular sheet are 16.2 cm and 10.1 cm, respectively. The area of the sheet in appropriate significant figures and error is:

  1. $164 \pm 3 cm^2$
  2. $163.62 \pm 2.6 cm^2$
  3. $163.6 \pm 2.6 cm^2$
  4. $163.62 \pm 3 cm^2$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the length and breadth of a rectangular sheet are measured by using a meter scale as 16.2 cm and 10.1 cm respectively. Each measurement has three significant figures.
$\therefore$ Length l can be written as
$l = 16.2 \pm 0.1 cm = 16.2 cm \pm 0.6$%

Similarly, the breadth b can be written as
$b = 10.1 \pm 0.1 cm = 10.1 cm \pm 1$%

Area of the sheet,
$A = l \times b = 163.62 cm^2 \pm 1.6% =163.62 \pm 2.6 cm^2$
Therefore, as per rule, the area will have only three significant figures and errors will have only one significant figure.
Rounding off, we get $A = 164 \pm 3 cm^2$

Multiple choice physics units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The length,breadth and thickness of a rectangular copper sheet are $4 cm, 2.5 cm $ and $1.56 cm $ respectively. Find the area of the sheet to corrected significant figures.

  1. $40.3 cm^2$
  2. $40.28 cm^2$
  3. $40 \times 10^2 cm^2$
  4. $0.4\times 10^2 cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If $l$ be the length, $b$ be the breadth and $t$ be the thickness of the sheet,
then the area of sheet is $A=2(lb+bt+tl)=2[(4\times 2.5)+(2.5\times 1.56)+(1.56\times 4)]=40.28 cm^2$
As length has least significant figures i.e one so the answer must be expressed as one significant figures. 
Thus according rule of determining significant figures, the area will be $0.4\times 10^2 cm^2$

Multiple choice maths average arithmetic mean of ap introduction to averages means

A boy draws n squares with sides $1,2,3,4,5....$ in inches.The average area covered by these n squares  will be:  

  1. $\left(\dfrac{n+1}{2}\right)$
  2. $\left(\dfrac{n+1}{2}\right)\left(\dfrac{2n+1}{3}\right)$
  3. $\left(\dfrac{n+1}{2}\right)\left(\dfrac{2n+1}{3}\right)^{-1}$
  4. $\left(\dfrac{n+1}{2}\right)-1 \left(\dfrac{2n+1}{3}\right)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Multiple choice

A rectangular room is 12 feet long and 8 feet wide. What is the area of the room in square feet?

  1. 96

  2. 104

  3. 112

  4. 120
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of the room = Length x Width Area = 12 feet x 8 feet = 96 square feet.

Multiple choice

A rectangular room is 12 feet long and 8 feet wide. What is the area of the room in square feet?

  1. 96

  2. 104

  3. 112

  4. 120
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of the room = Length x Width Area = 12 feet x 8 feet = 96 square feet.

Multiple choice

A rectangular garden has a length of 20 meters and a width of 15 meters. What is the area of the garden?

  1. 300 square meters

  2. 350 square meters

  3. 400 square meters

  4. 450 square meters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a rectangle is given by the formula A = l * w. Plugging in the values from the question, we get A = 20 * 15 = 300 square meters.

Multiple choice

A rectangular garden has a length of 20 meters and a width of 15 meters. What is the area of the garden?

  1. 300 square meters

  2. 350 square meters

  3. 400 square meters

  4. 450 square meters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a rectangle is given by the formula A = l * w. Plugging in the values from the question, we get A = 20 * 15 = 300 square meters.

Multiple choice

A rectangular garden has a length of 12 meters and a width of 8 meters. What is the area of the garden in square meters?

  1. 96

  2. 104

  3. 112

  4. 120
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a rectangle is given by length * width. Substituting the given values, we get the area as 12 meters * 8 meters = 96 square meters.

Multiple choice

A rectangular garden has a length of 12 meters and a width of 8 meters. What is the perimeter of the garden in meters?

  1. 40

  2. 48

  3. 56

  4. 64
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The perimeter of a rectangle is given by 2 * (length + width). Substituting the given values, we get the perimeter as 2 * (12 meters + 8 meters) = 2 * 20 meters = 40 meters.

Multiple choice

A rectangular garden has a length of 10 meters and a width of 8 meters. What is the area of the garden?

  1. 60 square meters

  2. 80 square meters

  3. 100 square meters

  4. 120 square meters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of a rectangle is calculated by multiplying its length and width. Therefore, the area of the garden is 10 meters * 8 meters = 80 square meters.

Multiple choice

A rectangular room has a length of 6 meters and a width of 4 meters. What is the perimeter of the room?

  1. 16 meters

  2. 20 meters

  3. 24 meters

  4. 28 meters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The perimeter of a rectangle is the sum of the lengths of all four sides. Therefore, the perimeter of the room is 2 * (length + width) = 2 * (6 meters + 4 meters) = 20 meters.

Multiple choice

A rectangular garden has a length of 12 meters and a width of 8 meters. What is the area of the garden in square meters?

  1. 96 square meters

  2. 104 square meters

  3. 112 square meters

  4. 120 square meters
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a rectangle is calculated by multiplying its length and width. Therefore, the area of the garden is 12 meters * 8 meters = 96 square meters.

Multiple choice

A rectangular garden has a length of 20 meters and a width of 15 meters. If a path of uniform width x meters is constructed around the garden, what is the area of the path?

  1. 350 + 100x square meters

  2. 400 + 100x square meters

  3. 450 + 100x square meters

  4. 500 + 100x square meters
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The area of the path can be calculated by subtracting the area of the garden from the area of the larger rectangle formed by the garden and the path. The area of the garden is 20 * 15 = 300 square meters. The length of the larger rectangle is 20 + 2x meters, and the width is 15 + 2x meters. Therefore, the area of the larger rectangle is (20 + 2x) * (15 + 2x) = 400 + 100x + 4x^2. Subtracting the area of the garden, we get the area of the path: 400 + 100x + 4x^2 - 300 = 400 + 100x square meters.

Multiple choice

A rectangular room has a length of 12 meters and a width of 8 meters. What is the area of the room in square meters?

  1. 96

  2. 104

  3. 112

  4. 120
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of the room is simply the length multiplied by the width. Therefore, the area of the room is 12 * 8 = 96 square meters.