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 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

If the difference between the circumference and radius of a circle is 37 cm, then the area of the circle is

  1. $111 cm^2$
  2. $148 cm^2$
  3. $259 cm^2$
  4. $154 cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Consider the difference between circumference and radius.


Taking$\pi $ as $3.14$ will give an approximate answer. we can do it by taking $22/7$ as wel


Let, the radius be$ r cm$


Circumference will be,

$2r=2\times 3.14r=6.28r$


ATQ,  $6.28r-1.r=37$

$5.28r=37$

 $r=\dfrac{37}{5.28}$

$r=$approx. $7 cm$ 

Area$=\pi {{r}^{2}}=3.14\times 7\times 7=154c{{m}^{2}}$


Hence, this is the answer.

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 units and measurement: error analysis significant figures significant figures and rounding of digits units and measurements

The length,breadth and thickness of a rectangular copper sheet are $4 cm, 2.5 cm $ and $1.56 cm $ respectively. Find the area of the sheet to corrected significant figures.

  1. $40.3 cm^2$
  2. $40.28 cm^2$
  3. $40 \times 10^2 cm^2$
  4. $0.4\times 10^2 cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

If $l$ be the length, $b$ be the breadth and $t$ be the thickness of the sheet,
then the area of sheet is $A=2(lb+bt+tl)=2[(4\times 2.5)+(2.5\times 1.56)+(1.56\times 4)]=40.28 cm^2$
As length has least significant figures i.e one so the answer must be expressed as one significant figures. 
Thus according rule of determining significant figures, the area will be $0.4\times 10^2 cm^2$

Multiple choice

A rectangular room is 12 feet long and 8 feet wide. What is the area of the room in square feet?

  1. 96

  2. 104

  3. 112

  4. 120
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of the room = Length x Width Area = 12 feet x 8 feet = 96 square feet.

Multiple choice

A rectangular room is 12 feet long and 8 feet wide. What is the area of the room in square feet?

  1. 96

  2. 104

  3. 112

  4. 120
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of the room = Length x Width Area = 12 feet x 8 feet = 96 square feet.