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

The length of a rectangle is thrice its breadth. If its length is increased by 4 cm and the breadth is decreased by 3 cm, the area of the rectangle is decreased by 77 cm2. Therefore, the length of the rectangle is

  1. 20 cm

  2. 30 cm

  3. 39 cm

  4. 40 cm

  5. 24 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let breadth =x cm and length = 3x cm Then, original area = x*3x = 3x2 cm2, After changing into dimensions, Area = (3x + 4)*(x – 3) = 3x2 – 5x - 12 So, 3x2 – (3x2 – 5x – 12) = 77, 5x + 12 = 77 x = 13, Length = 3*13 = 39 cm.

Multiple choice

A rectangular field with length 70 m is to be fenced on three sides leaving a length of 10 m for entering in the field. If the area of the field is 3150 sq. m, how many metres of fencing will be required?

  1. 210 m

  2. 220 m

  3. 200 m

  4. 215 m

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

It is given that length = 70 m. Then, breadth = area/length Breadth = 3150/70 = 45 m Now, perimeter of the rectangle = 2(70 + 45) = 230 m So, the quantity of fencing that will be required = 230 - 10 = 220 m.

Multiple choice

In measuring the sides of a rectangle, it is found that the length is 4% in excess and the breadth is 3% in deficit. Find the error percentage in the area.

  1. 0.88% increase

  2. 0.55% increase

  3. 0.99% increase

  4. 0.89% increase

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

Let the length of rectangle = 10 and breadth = 10, then area = 10 x 10 = 100. Now, if 4% in excess in length and 3% in deficit in breadth, then area = 10.4 x 9.7 = 100.88. Increase in area = 100.88 - 100 = 0.88 Now, percentage error = 0.88%

Multiple choice

If the ratio of the areas of two squares is 225 : 256, then the ratio of their perimeters is

  1. 225 : 256

  2. 60 : 64

  3. 24 : 26

  4. 15 : 16

  5. -
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

This is the correct answer. Let the side of square 1 be s1 and that of square 2 be s2. So, the ratio of their areas is (s1)2 : (s2)2 = 225 : 256 (s1)2 : (s2)2 = (15)2 : (16)2 So, s1 = 15, s2 = 16 So, the ratio is 15 : 16. The ratio of their perimeters is 4 x 15 : 4 x 16 = 60 : 64 = 15 : 16.

Multiple choice

If the side of a square is tripled, what will happen to its area?

  1. It will increase 4 times.

  2. It will increase 6 times.

  3. It will increase 9 times.

  4. It will increase 12 times.

  5. -
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is the correct answer. If the side of the square is tripled, new side = 3x Area = (3x) X 3x = 9x2 The area will be increased 9 times.

Multiple choice

If the length of a rectangle is decreased by 30% and the breadth is increased by 50%, then find the change in area of the rectangle.

  1. 20% increase

  2. 80% increase

  3. 5% decrease

  4. 5% increase

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

Let the length be l and the breadth be b. Original area = l * b Now, new length = 0.7 * l and new breadth = 1.5 * b So, new area = (0.7 * 1.5 * l * b) = 1.05 * l * b Change in area = 5%(increase) Hence, this option is correct.