Mathematics

Area and Perimeter

170 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

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.

Multiple choice

The area of a square is 2304 m2. Its one side is equal to the breadth of a rectangle and its length is double of its breadth. Find the perimeter of the rectangle.

  1. 288 m

  2. 3456 m

  3. 663552 m

  4. 4608 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

 Area of square is 2304 m2 one side of square is square root of 2304
                          =48 m
 
 
one side of square is equal to the breadth of rectangle

so breadth of rectangle is  =48 m

length of rectangle is double of breadth=2x48                                                                       =96m
 
perimeter of rectangle = 2 x (l + b )                                       =2x ( 48 + 96 )
                                        = 2 x 144                                         = 288 m

 

Multiple choice

Ganga has a square chart paper of side 13 cm and a colourful circular sticker of radius 7 cm. What is the area and perimeter of the chart paper and the colourful sticker (respectively)?

  1. 44 cm; 169 sq. cm

  2. 169 sq. cm; 44 cm

  3. 52 cm; 154 sq. cm

  4. 52 sq. cm; 154 cm

  5. 170 sq. cm; 50 cm
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

This is the right answer because the side of the square chart paper = 13 cm Area of the square chart paper = side * side                            = 13 cm * 13 cm = 169 sq. cm Radius of the colourful sticker = 7 cm Perimeter or circumference of the sticker = 2 * pi * radius                                             = 2 * 22/7 * 7 = 44 cm Perimeter or circumference of the sticker = 44 cm

Ans: 169 sq. cm; 44 cm