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 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 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 properties of parallel lines and their transversal how to check for similarity in triangles? criteria for similarity of triangles criteria for triangle similarity

If $\displaystyle \triangle ABC\sim \triangle DEF$ BC=4 cm, EF=5 cm and ar $\displaystyle \left ( \triangle ABC \right )=80cm2$,the ar$\displaystyle \left ( \triangle DEF \right )$ is

  1. $\displaystyle 120cm^{2}$
  2. $\displaystyle 125cm^{2}$
  3. $\displaystyle 150cm^{2}$
  4. $\displaystyle 200cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

If two triangles are equals than the ratio of their square is equal to the ratio of their corresponding sides.

$\therefore \dfrac{arc(\triangle ABC)}{arc(\triangle DEF)}=\dfrac{BC^2}{EF^2}$
$\Rightarrow \dfrac{80}{arc(\triangle DEF)}=\dfrac{16}{25}$
$\Rightarrow arc(\triangle DEF)=\dfrac{80\times 25}{16}=125 cm^2$


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.

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,

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