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

What is the maximum area of a four-sided plane with a perimeter of $12$ inches?

  1. $8$ square inches
  2. $10$ square inches
  3. $6$ square inches
  4. $9$ square inches
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

The area is maximum when the four-sided plane is a square.

The perimeter of a square $ = 4 \times$ side $= 12 $ inches
$ \Rightarrow$ side $= 3  $ inches

Now, area of the square $ =$ side $\times$ side $= 3 \times 3 = 9 $ square inches.

Multiple choice maths enlargement and scale drawing dilation enlargement similarity as a size transformation mapping mapping space around us bearing and drawings

A rectangle of length $4\ cm$ and breadth $3\ cm$ is scaled up $2$ times. What is the new length of the rectangle?

  1. $6\ cm$
  2. $4\ cm$
  3. $8\ cm$
  4. $3\ cm$
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The size of the rectangle become double when it is scaled up $2$ times.

So new length $=2\times 4=8\ \ cm$
So option $C$ is correct.

Multiple choice maths circle measures length of an arc area of a sector of a circle sector and arc of a circle

The perimeter and area of a sector are $18\;cm$ and $20\;sq.\,cm$ respectively. Then the length of the arc is:

  1. $10\;cm\;or\;8\;cm$
  2. $10\;cm\;or\;5\;cm$
  3. $10\;cm\;or\;4\;cm$
  4. $20\;cm\;or\;2\;cm$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

$l+2r=18$
$\displaystyle\frac{lr}{2}=20$
$lr=40$
$l=\displaystyle\frac{40}{r}$
$18=\displaystyle\frac{40}{r}+2r$
$r^2-9r+20=0$
$(r-4)\;\;(r-5)=0$
$r=4$ or $r=5$
$l=8$ or $l=10\;cm$

Multiple choice maths construction circumscribing and inscribing a circle on a regular hexagon construction of tangent to a circle construction of tangents construction of line segment and circle of given radius construction related to lines

The minimum number of dimensions needed to construct a rectangle is:

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

We can construct a rectangle when:

(i) two adjacent sides are given
(ii) one side and the diagonal is given
(iii) both diagonals are given
In the above cases the number of dimensions needed to construct a rectangle is $2$.

Multiple choice maths real number real numbers on number line fundamental theorem of arithmetic common factors and hcf

A rectangular veranda is of dimension $18$m $72$cm $\times 13$ m $20$ cm. Square tiles of the same dimensions are used to cover it. Find the least number of such tiles.

  1. $4290$
  2. $4540$
  3. $4620$
  4. $4230$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The edge of rectangular veranda are $18\ m\ 72\ cm=1872\ cm$ and $13\ m\ 20\ cm=1320\ cm$.


On taking $HCF$ of $1872$ and $1320$, we get

$HCF=24$

Therefore,
No. of tiles required $=$ $\dfrac{Area\ of\ Veranda}{Area\ of\ tiles}$

                                  $=\dfrac{1872\times 1320}{24\times 24}$

                                  $=4290$

Hence, this is the answer.