Mathematics

Parallelogram Properties and Area

93 Questions

Parallelogram properties and area questions test the ability to calculate dimensions using base and height ratios. Problems also cover diagonal properties and internal angles. These geometry concepts regularly appear in quantitative aptitude sections of various exams.

Area calculationBase and height ratiosDiagonal propertiesInterior anglesGeometric theorems

Parallelogram Properties and Area Questions

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

A rectangle and a parallelogram have equal areas. If the sides of the rectangle are $10 m$ and $12 m$ and the base of the parallelogram is $20 m$, then the altitude of the parallelogram is:

  1. $7 m$
  2. $6 m$
  3. $5 m$
  4. $3 m$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Area of the rectangle $= l \times b = 10 m \times 12 m$
                                     $= 120 m^{2}$
Area of parallelogram $= Base \times Altitude= 120 m^{2}$
$ \Rightarrow$ Altitude $= \cfrac{Area }{Base}=\cfrac{120m^{2}}{20m}=6m$

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

A rectangle and a parallelogram have equal areas. The base of the parallelogram is $20 cm$ and the altitude is $6 cm$. Which one of the following cannot be the ratio of dimensions of the rectangle?

  1. $7 : 5$
  2. $40 : 3$
  3. $15 : 2$
  4. $30 : 1$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Area of the rectangle $=$ Area of parallelogram
                                     $= 20 cm \times 6 m = 120 \displaystyle cm^{2}$
Now,                 
Ratio $= 7 : 5$             Ratio $= 40 : 3$
Product $= 35$            Product $= 120$
-------------------------------------------------------------
Ratio $= 15 :2$           Ratio $= 30 : 1$
Product $= 30$            Product $= 30$
$\displaystyle \therefore $ Ratio $= 7 : 5$ does not match with the condition as $120$ is not divisible by $35$.

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

One side of a parallelogram is 8 cm If the corresponding altitude is 6 cm then its area is given by

  1. 24 $ \displaystyle cm ^{2} $
  2. 36 $ \displaystyle cm ^{2} $
  3. 40 $ \displaystyle cm ^{2} $
  4. 48 $ \displaystyle cm ^{2} $
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Given One side of parallelogram is 8 cm and altitude is 6 cm 

Here base=8 cm and height(altitude)=6 cm
We know that area of parallelogram=$base \times hieght$

Here base=8 cm and height(altitude)=6 cm
Then area of  parallelogram=$8\times 6=48 cm^{2}$

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

The height of a parallelogram of area $ \displaystyle   350 cm^{2}   $ and base 25 cm is

  1. 12 cm

  2. 13 cm

  3. 14 cm

  4. 15 cm
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given the area of parallelogram is 350 sq cm and base is 25 cm

Then area of  parallelogram if height h and base 25
$\therefore 350=base \times height\Rightarrow 25\times h=350\Rightarrow h=14$ cm

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

Two adjacent sides of a parallelogram are x and y and the included angle is $\displaystyle \alpha  $ then the area of the parallelogram is

  1. xy $\displaystyle \cot \alpha $
  2. xy $\displaystyle \cos \alpha $
  3. xy $\displaystyle \sin \alpha $

  4. none of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Given the two adjacent sides of a parallelogram is x and y and angle is $\alpha $

let the height of  parallelogram is h
Then $sin \alpha=\frac{h}{y}\Rightarrow h=y sin \alpha  $

So area of   parallelogram=$base\times heigth=x\times ysin\alpha =xy sin\alpha $

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

Find the area of the parallelogram whose base is 16 cm and height 0.4 m ?

  1. 440 $cm^2$
  2. 740 $cm^2$
  3. 640 $cm^2$

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

Base = 16 cm
Height = 0.4 m
            = 0.4 $\times$ 100 = 40 cm
Area of parallelogram = b $\times$ h
                                      = 16 $\times$ 40
                                      = 640 $cm^2$

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

In a parallelogram the base and height are is in the ratio of $5 : 2$. If the area of the parallelogram is $360\ m^{2}$, find its base and height.

  1. $30\ m, 12\ m$.
  2. $20\ m, 12\ m$.
  3. $30\ m, 10\ m$.

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

Area = base * height = 360. Given base:height = 5:2, let base = 5x and height = 2x. Then 10x^2 = 360, so x^2 = 36, x = 6. Base = 30m, height = 12m.

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

One side of a parallelogram is $8$ cm. If the corresponding altitude is $6$ cm, then its area is given by

  1. $24\: cm^2$
  2. $36\: cm^2$
  3. $40\: cm^2$
  4. $48\: cm^2$
Reveal answer Fill a bubble to check yourself
D Correct answer
Explanation

Area of parallelogram $=$ length $\times$ height
Here altitude is nothing but the height
$\therefore $ Area of parallelogram $= 8 \times 6$
$= 48: cm^2$

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

$A, B, C, D$ are mid points of sides of parallelogram $PQRS$. If $ar(PQRS)=36\ cm^{2}$ then $ar(ABCD)$

  1. $24\ cm^{2}$
  2. $18\ cm^{2}$
  3. $30\ cm^{2}$
  4. $36\ cm^{2}$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation
$A,B,C,D$ are point of sides of parallelogram $PQRS$ area $(PQRS)=36\ cm^2 ar (ABCD)=?$
$AP=\dfrac {1}{2}SP,\ BP=\dfrac {1}{}QR$
$PS=QR, \dfrac {1}{2}PS=\dfrac {1}{2} QR$
area $(\triangle ABC)=\dfrac {1}{2} (\triangle PQCQ)$
area $(\triangle ADC)=\dfrac {1}{2} ar (ACRS)$
area $\triangle ABC+area (\triangle ADC)=\dfrac {1}{2} area (APCQ)=\dfrac {1}{2}area (ACRS)$
$area (ADCD)=\dfrac {1}{2}area (APCQ)+(ACRS)area $
$area (ABCD)=\dfrac {1}{2} area (PQRS)$
$area (ABCD)=\dfrac {1}{2} (36)$
$=18\ cm^2$


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

A parallelogram has sides $30m$ and $14m$ and one of its diagonals is $40m$ long. Then, its area is:

  1. $168{m}^{2}$
  2. $336{m}^{2}$
  3. $372{m}^{2}$
  4. $480{m}^{2}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation
Area of parallalogram = $2\times area of triangle $
Area of triangle where three sides a,b,c are given is $\sqrt{s(s-a)(s-b)(s-c)}$, where $s=\dfrac{a+b+c}{2}$
Here $s=\dfrac{30+14+40}{2}=42$
$Area\ of \triangle=\sqrt{(42)(12)(28)(2)}=\sqrt{28224}=168m^2$
Therefore area of parallalogram = $336 m^2$
Hence option B is correct