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 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

Multiple choice

The length and breadth of a lawn are 60 m and 50 m. If this lawn is to be divided into 4 equal parts, then what is the perimeter of each part of the lawn?

  1. 55 sq. m

  2. 55 m

  3. 110 m

  4. 220 m

  5. 880 m
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

This is the right answer. Length of the lawn = 60 m Breadth of the lawn = 50 m Length of each part of the lawn = 30 m. Breadth of each part of the lawn = 25 m. Perimeter of each part of the lawn = 2(length + breadth)                        = 2(30 + 25)m =2 * 55 m = 110 m

Multiple choice

Which of the following is correct if the length and breadth of a rectangle are doubled and halved, respectively?

  1. Only perimeter would remain same

  2. Area is increased by a factor of 2

  3. Area would remain same

  4. Perimeter and Area both will remain same

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

Let length of the rectangle is A New length = 2A Let breadth of the rectangle is B New Breadth = B/2 New Area = A x B = AB (Same as old area) New perimeter = 2(2A+B/2) = 4A +B

This is a right answer.

Multiple choice

A goat is tied to one corner of a square plot of side 12m by a rope 7m long.Find the area it can graze?

  1. 38.5 sq.m

  2. 155 sq.m

  3. 144 sq.m

  4. 19.25 sq.m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The goat is tied to a corner with a 7m rope. In a square corner, the goat can graze a quarter-circle of radius 7m. Area of quarter-circle = (1/4) × π × r² = (1/4) × π × 49 = 49π/4 ≈ 38.48 square meters. This matches Option A (38.5 sq.m, accounting for rounding).

Multiple choice

The perimeter of a rectangular whiteboard is 14 m and its width is a m. What would be the perimeter of a new whiteboard whose length is 2 m more than the length of the older whiteboard?

  1. 18 m

  2. 9 m

  3. 22 m

  4. 10 m

  5. 16 m
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Let the length of the whiteboard be l m and width of the whiteboard be a m. Perimeter of the whiteboard = 14 m 2(l + w) = 14 Now, the length of the new whiteboard is (2 + l) m and width of the whiteboard is a m. Hence, the perimeter of the new whiteboard = 2(L + w) = 2(2m + l m + w m)                                                                                 = 4m + 2(l + w)                                                                                 = 4m + 14m = 18 m

Multiple choice

If the perimeter of an equilateral triangle is 18 cm and the side of a square is equal to the side of the given equilateral triangle. Then what is the perimeter of the rectangle whose length is equal to the diagonal of the square and the breadth is equal to side of the equlilateral triangle.

  1. 12(1 + 1.732) cm

  2. 6(1 + 1.732) cm

  3. 6(1 + 1.414) cm

  4. 12(1 + 1.414) cm

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

Length of rectangle 6 x 1.414 cm Breadth = 6 cm