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

Directions: The following problem has a question and two statements labelled (1) and (2). You have to decide whether the statements are sufficient to answer the question. Mark your answer as

Mr. Carpenter wants to build a room in the shape of a rectangle. The area of the floor will be 32 square feet. What is the length of the floor? (1) The length of the floor will be twice the width of the floor. (2) The width of the floor will be 4 feet less than the length of the floor.

  1. if you can get the answer from (1) alone, but not from (2) alone

  2. if you can get the answer from (2) alone, but not from (1) alone

  3. if you can get the answer from (1) and (2) together, although neither statement by itself suffices

  4. if (1) alone suffices and (2) alone suffices

  5. if you cannot get the answer from (1) and (2) together, and need even more data

Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Correct option is (4).

Multiple choice maths area of complex plane figures 2d and 3d figures

A rectangular sheet of acrylic is 50 cm by 25 cm . From it 60 circular buttons, each of diameter 2.8 cm have been cut out. The area of the remaining sheet is

  1. 1260.82 $\displaystyle cm^{2}$
  2. 880.4 $\displaystyle cm^{2}$
  3. 630.4 $\displaystyle cm^{2}$

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

Required area
= Area of sheet - 60 $\displaystyle \times $ area of 1 button
$\displaystyle=\left ( 50\times 25-60\times \dfrac{22}{7}\times 1.4\times 1.4 \right )cm^{2}$
$\displaystyle =\left ( 1250-369.6 \right )cm^{2}$
$\displaystyle =880.4cm^{2}$

Multiple choice maths area and its boundary unit of area units of area units of area and volume

The area of square is equal to area of rectangle with length$8mm$ and breadth$2m$.Find its area in $cm^2$

  1. $160cm^2$
  2. $1.6cm^2$
  3. $.16cm^2$
  4. $none$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Rectangle area = 8 mm * 2 m = 0.8 cm * 200 cm = 160 cm^2. Since the square has the same area, the square's area is 160 cm^2.

Multiple choice maths geometrical construction constructing perpendicular lines perpendicular to a line from an external point constructing an perpendicular line constructing a perpendicular bisector construction of a perpendicular bisector construction of penpendicual bisector set squares

There is a rectangular sheet of dimension $(2m-1)\times (2n-1)$, (where $m > 0, n > 0$). It has been divided into square of unit area by drawing lines perpendicular to the sides. Find number of rectangles having sides of odd unit length?

  1. $(m+n+1)^2$
  2. $mn(m+1)(n+1)$
  3. $4^{m+n-2}$
  4. $m^2n^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Total no. of horizontal line=2m

Total no. of vertical lines=2n
($\because$ Each line is at unit distance and hence, total no. of lines=Distance/lenght +1).
To form a square from three lines,we must select one even and one odd numbered horizontal and vertical line.
$\therefore$ Ways possible of selecting such squares=$({ C } _{ 1 }^{ m }\times { C } _{ 1 }^{ m })\times ({ C } _{ 1 }^{ n }\times { C } _{ 1 }^{ n })$
$ ={ C } _{ 1 }^{ m }\times { C } _{ 1 }^{ m }\times { C } _{ 1 }^{ n }\times { C } _{ 1 }^{ n }$
$ ={ m }^{ 2 }\times { n }^{ 2 }$
$ ={ m }^{ 2 }{ n }^{ 2 }$

Multiple choice maths how many squares area of rectangular paths comparing areas spaces and boundaries - 2

A square of side x is taken A rectangle is cut out from this square such that one side of the rectangle is half that of the square and the other is $\displaystyle \frac{1}{3}$ of the first side of the rectangle
What is the area of the remaining portion?

  1. $\displaystyle \left ( \frac{3}{4} \right )x^{2}$
  2. $\displaystyle \left ( \frac{7}{8} \right )x^{2}$
  3. $\displaystyle \left ( \frac{11}{12} \right )x^{2}$
  4. $\displaystyle \left ( \frac{15}{16} \right )x^{2}$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Let the side of square is x 

Then area of square=$x^{2}$
Given one side of rectangle is half of square=$\frac{x}{2}$
And second side is $\frac{1}{3}$ of other side=$\frac{1}{3}\times \frac{x}{2}=\frac{x}{6}$
Then area of rectangle =$\frac{x}{2}\times \frac{x}{6}=\frac{(x)^{2}}{12}$
So remaining area of square =$x^{2}-\frac{(x)^{2}}{12}=\frac{11x^{2}}{12}$