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 maths bar graphs histograms for non-uniform class widths histograms with unequal class intervals revisiting histograms

In a histogram, the area of each rectangle is proportional to the class size of the corresponding class interval? If not, correct the statement.
If true then enter $1$ and if false then enter $0$

  1. $1$
  2. $0$

  3. can't determine

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

No, this is not a correct statement.
In a histogram, horizontal axis represents the class intervals whose width is fixed & the varying data is plotted along the y-axis. So in all  the rectangles of a histogram, width remains same & the length changes.
So correct statement is "In a histogram, the area of each rectangle is proportional to the frequency of its class."

Multiple choice maths surface area and volume of cube and cuboid length of the diagonal diagonal of cube and cuboid surface area of cubes and cuboids

Instead of walking along two adjacent sides of a rectangular field, a boy took a short cut along the diagonal and saved the distance equal to half of the longer side. Then the ratio of the shorter side to the longer side is?

  1. $\cfrac{2}{3}$
  2. $\cfrac{5}{3}$
  3. $\cfrac{4}{3}$
  4. $\cfrac{8}{3}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Atp,

$\sqrt{l^2+b^2} + \cfrac{l}{2} = l+b$
$\sqrt{l^2+b^2} = b+\cfrac{l}{2}$
$l^2+b^2 = b^2+2lb+\cfrac{l^2}{4}$
$\cfrac{3l^2}{4} = 2lb$
$\cfrac{l}{b} = \cfrac{8}{3}$

Multiple choice maths perimeter and area of rectilinear figures parallelogram and rectangle area of parallelogram area of a parallelogram

The area four walls of a hall is $320\ m^{2}$. The length & breadth of the hall is $12.5\ m$ & $7.5\ m$ respectively, Find the height of the hall.

  1. $32\ m$
  2. $9\ m$
  3. $3\ m$
  4. $5\ m$
  5. $None\ of\ these$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
formula,

$\dfrac{(l+b)h}{2}=area$

$\dfrac{(12.5+7.5)h}{2}=320$

$(12.5+7.5)h=640$

$20h=640$

$\therefore h=32m$

Multiple choice maths circle measures area between two concentric circles the area of ring semicircle and ring

A dog is chained on a $6\ ft$ leash, fastened to the corner of a rectangular building. Calculate, about how much area does the dog have to move in.

  1. $27\ ft^{2}$
  2. $36\ ft^{2}$
  3. $56.55\ ft^{2}$
  4. $84.82\ ft^{2}$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

A dog is chained on a $6$ ft leash to the corner of a rectangular building.
Since the building is rectangular, the dog is left with an angle of $360 - 90 = 270^o$ for it to roam around.
Also, the length of the leash will act as the radius of this sector.
$\therefore$ Area of the sector $= \cfrac{270}{360} \times \pi \times 6^2$
$= \cfrac{3}{4} \times \pi \times 36$
$= 84.82 \ \ ft^2$

Multiple choice maths fun with numbers some special sequences triangular numbers properties and patterns of perfect squares

A rectangle with integer side length has perimeter $10$. What is the greatest numbers of these rectangles that can be cut from a piece of paper with width $24$ and length $60$?

  1. $144$
  2. $180$
  3. $240$
  4. $360$
  5. $480$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If a rectangle has perimeter 10 then the sum of its length and width is 5, giving two choice with integer sides:

$(i)2\times3$ rectangle of area $6$
$(ii)1\times4$ rectangle of area $4$
The piece of paper has area $24\times60=1400$
This can be divided into $12\times20=240$ rectangles with sides $2\times3$
It can be divided into $24\times15=360$ recatngles with sides $1\times4$
So, the greatest number of rectangles is $360$

Multiple choice maths ratio, proportion and unitary method converting to ratios finding ratios other quantities

The length and breadth of a rectangular field are $50\ m$ and $15\ m$ respectively. Find the ratio of the breadth to the length of the field.

  1. $3:5$
  2. $3:10$
  3. $3:15$
  4. $10:3$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

The length of the rectangular field is $50 m$ and breadth of the field is $15 m$.

The ratio of breadth and length is,

${\rm{breadth}}:{\rm{length}} = 15:50=\dfrac{15}{50}=\dfrac{3}{10}$

$ = 3:10$

Multiple choice

A side of a square which area is 100km2 is

  1. 100km

  2. 104m

  3. 10-1km

  4. 105m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

For a square with area 100km², each side is √100 = 10km = 10,000m. Option B correctly states this as 10^4 m (which equals 10,000m).

Multiple choice maths square root square root of perfect square finding square root of a number square root of a perfect square

Find the length of the side of a square whose area is 441 $ \displaystyle m^{2} $.

  1. $19 $ m
  2. $21 $ m
  3. $23 $ m
  4. $29 $ m
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given the area of the square is $441\ m^2$ .

We know the area of the square is side$^{ 2 }$
So, the square root of side is $\sqrt { 441 } =\sqrt{3\times\ 3\times 7\times 7}=3\times 7=21$.
The side of the square is $21$ m.

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The length and breadth of a rectangular object are 25.2 cm and 16.8 cm respectively and have been measured to an accuracy of 0.1 cm. The relative error and percentage error in the area of the object are:

  1. 0.01 ; 1%

  2. 0.1 ; 10%

  3. 1 ; 10 %

  4. 1 ; 100 %
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$Area  = l\times b$

$\dfrac { \triangle A }{ A } =\dfrac { \triangle l }{ l } +\dfrac { \triangle b }{ b }$


           $ = (\dfrac{0.1}{25.2} + \dfrac{0.1}{16.8})=0.00992\approx0.01$


This is the relative error.

Percentage  error $ =  0.01 \times 100  =  1\%$

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

In a measurement, the uncertainty of length $L$ is $\pm a$ and the uncertainty of width $W$ is $\pm b$. Assuming a and b very small, find the the uncertainty in measurement of area. 

  1. $a/L+b/W$
  2. $aL+bW$
  3. $aW+bL$
  4. $a^2/W+b^2/L$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Here given, $\Delta L=a$ and $\Delta W=b$
Area, $A=LW$
Take ln and then differentiate, $\dfrac{\Delta A}{A}=\dfrac{\Delta L}{L}+\dfrac{\Delta W}{W}=a/L+b/W$
So,$\Delta A=(a/L+b/W)(LW)=aW+bL$

Multiple choice physics measurements and experimentation vernier calliper and screw gauge least count of vernier calliper and screw gauge measurement of length

The length  and width of a rectangular room are measured to be $3.95 \pm  0.05 m$ and $3.05 \pm  0.05m$, respectively. The area of the floor is 

  1. $12.05\pm 0.01m^2$
  2. $12.05\pm 0.005m^2$
  3. $12.05\pm 0.34 m^2$
  4. $12.05\pm 0.40m^2$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Length of the room  $l = 3.95 \pm 0.05 \ m$
Width of the room  $b = 3.05\pm 0.05 \ m$
Absolute area of the room  $A = lb = 3.95\times 3.05 = 12.05 \ m^2$
Error in area of room   $\dfrac{\Delta A}{A} = \dfrac{\Delta l}{l}+\dfrac{\Delta b}{b}$
$\therefore$   $\dfrac{\Delta A}{12.05} = \dfrac{0.05}{3.95}+\dfrac{0.05}{3.05}$
$\implies \ \Delta A = 0.34 \ m^2$
Thus area of the room is written as  $12.05\pm 0.34 \ m^2$