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

A rectangular garden has a length of 12 feet and a width of 8 feet. If a path of uniform width is constructed around the garden, increasing the length and width by 2 feet each, what is the area of the path?

  1. 32 square feet

  2. 48 square feet

  3. 64 square feet

  4. 80 square feet
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the area of the path, we need to calculate the area of the new garden (including the path) and subtract the area of the original garden. The new garden has a length of 12 + 2 + 2 = 16 feet and a width of 8 + 2 + 2 = 12 feet. Therefore, the area of the new garden is 16 x 12 = 192 square feet. The area of the original garden is 12 x 8 = 96 square feet. Subtracting the area of the original garden from the area of the new garden, we get 192 - 96 = 96 square feet. However, since the path surrounds the garden, we need to divide this value by 2 to get the area of the path, which is 96 / 2 = 64 square feet.

Multiple choice

A rectangular room is 12 feet long and 8 feet wide. If the perimeter of the room is 40 feet, what is the area of the room?

  1. 72 square feet

  2. 80 square feet

  3. 88 square feet

  4. 96 square feet
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The perimeter of a rectangle is the sum of the lengths of all four sides. In this case, the perimeter is 40 feet, so we have 2(12 feet + 8 feet) = 40 feet. Simplifying this equation, we get 20 feet + 16 feet = 40 feet. Subtracting 20 feet from both sides, we get 16 feet = 24 feet. Therefore, the area of the room is 12 feet x 8 feet = 96 square feet.

Multiple choice

A rectangular garden has a length of 15 feet and a width of 10 feet. If a path of uniform width is constructed around the garden, increasing the length and width by 2 feet each, what is the area of the path?

  1. 40 square feet

  2. 50 square feet

  3. 60 square feet

  4. 70 square feet
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the area of the path, we need to calculate the area of the new garden (including the path) and subtract the area of the original garden. The new garden has a length of 15 + 2 + 2 = 19 feet and a width of 10 + 2 + 2 = 14 feet. Therefore, the area of the new garden is 19 x 14 = 266 square feet. The area of the original garden is 15 x 10 = 150 square feet. Subtracting the area of the original garden from the area of the new garden, we get 266 - 150 = 116 square feet. However, since the path surrounds the garden, we need to divide this value by 2 to get the area of the path, which is 116 / 2 = 60 square feet.

Multiple choice

A rectangular room is 18 feet long and 12 feet wide. If the perimeter of the room is 60 feet, what is the area of the room?

  1. 180 square feet

  2. 200 square feet

  3. 220 square feet

  4. 240 square feet
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

The perimeter of a rectangle is the sum of the lengths of all four sides. In this case, the perimeter is 60 feet, so we have 2(18 feet + 12 feet) = 60 feet. Simplifying this equation, we get 30 feet + 24 feet = 60 feet. Subtracting 30 feet from both sides, we get 24 feet = 30 feet. Therefore, the area of the room is 18 feet x 12 feet = 216 square feet.

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. \(\$2x(20 + 15)\)
  2. \(\$2x(20 - 15)\)
  3. \(\$(20 + 15)x^2\)
  4. \(\$(20 - 15)x^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of the path is equal to the area of the outer rectangle minus the area of the inner rectangle. The outer rectangle has a length of (\$(20 + 2x)) meters and a width of (\$(15 + 2x)) meters. Therefore, the area of the outer rectangle is (\$(20 + 2x)(15 + 2x)) square meters. The inner rectangle has a length of 20 meters and a width of 15 meters. Therefore, the area of the inner rectangle is (\$20 \times 15) square meters. Therefore, the area of the path is (\$(20 + 2x)(15 + 2x) - 20 \times 15) square meters = (\$2x(20 + 15)) 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. \(\$2x(20 + 15)\)
  2. \(\$2x(20 - 15)\)
  3. \(\$(20 + 15)x^2\)
  4. \(\$(20 - 15)x^2\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of the path is equal to the area of the outer rectangle minus the area of the inner rectangle. The outer rectangle has a length of (\$(20 + 2x)) meters and a width of (\$(15 + 2x)) meters. Therefore, the area of the outer rectangle is (\$(20 + 2x)(15 + 2x)) square meters. The inner rectangle has a length of 20 meters and a width of 15 meters. Therefore, the area of the inner rectangle is (\$20 \times 15) square meters. Therefore, the area of the path is (\$(20 + 2x)(15 + 2x) - 20 \times 15) square meters = (\$2x(20 + 15)) square meters.

Multiple choice

A rectangular garden has a length of (x) meters and a width of (y) meters. If the area of the garden is (100) square meters, what is the perimeter of the garden?

  1. \(2x + 2y\)
  2. \(x + y\)
  3. \(2x - 2y\)
  4. \(x - y\)
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The area of a rectangle is given by (A = l \times w). Therefore, (100 = x \times y). The perimeter of a rectangle is given by (P = 2l + 2w). Substituting (x = \frac{100}{y}) into the formula for the perimeter, we get (P = 2 \left(\frac{100}{y}\right) + 2y = \frac{200}{y} + 2y = \frac{200 + 2y^2}{y}). Therefore, the perimeter of the garden is (\frac{200 + 2y^2}{y}).

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

The area of a rectangle is given by (length \times width). Therefore, the area of the room is (12 \times 8 = 96) square feet.

Multiple choice

A rectangular garden has a length of (x + 2) meters and a width of (x - 3) meters. If the area of the garden is 24 square meters, what is the value of x?

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The area of a rectangle is length * width. Therefore, (x + 2)(x - 3) = 24. Expanding the brackets, we get x^2 - x - 6 = 24. Rearranging, we get x^2 - x - 30 = 0. Factoring, we get (x - 6)(x + 5) = 0. Therefore, x = 6 or x = -5. Since the length of the garden cannot be negative, x = 6.

Multiple choice

A rectangular room has a length of 12 feet and a width of 8 feet. 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

The area of a rectangle is length * width. Therefore, the area of the room is 12 feet * 8 feet = 96 square feet.

Multiple choice

A rectangular garden has a length of (x + 2) meters and a width of (x - 3) meters. If the area of the garden is 24 square meters, what is the value of x?

  1. 3

  2. 4

  3. 5

  4. 6
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The area of a rectangle is length * width. Therefore, (x + 2)(x - 3) = 24. Expanding the brackets, we get x^2 - x - 6 = 24. Rearranging, we get x^2 - x - 30 = 0. Factoring, we get (x - 6)(x + 5) = 0. Therefore, x = 6 or x = -5. Since the length of the garden cannot be negative, x = 6.

Multiple choice

A rectangular garden has a length of 10 meters and a width of 5 meters. What is the area of the garden?

  1. 20 m²

  2. 25 m²

  3. 30 m²

  4. 35 m²
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 10 meters and the width is 5 meters, so the area is 10 meters * 5 meters = 50 square meters.

Multiple choice

A rectangular garden has a length of 10 meters and a width of 5 meters. What is the area of the garden?

  1. 20 m²

  2. 25 m²

  3. 30 m²

  4. 35 m²
Reveal answer Fill a bubble to check yourself
Correct answer
Explanation

The area of a rectangle is calculated by multiplying its length by its width. In this case, the length is 10 meters and the width is 5 meters, so the area is 10 meters * 5 meters = 50 square meters.

Multiple choice

Find the area of a rectangle with length 8 cm and width 6 cm.

  1. 24 cm^2

  2. 32 cm^2

  3. 40 cm^2

  4. 48 cm^2
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

To find the area of a rectangle, multiply the length by the width: Area = length x width = 8 cm x 6 cm = 48 cm^2. Therefore, the answer is 48 cm^2.

Multiple choice

What is the perimeter of a square with side length 10 cm?

  1. 20 cm

  2. 30 cm

  3. 40 cm

  4. 50 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

To find the perimeter of a square, multiply the side length by 4: Perimeter = 4 x side length = 4 x 10 cm = 40 cm. Therefore, the answer is 40 cm.