Tag: perimeter and area of rectilinear figures

Questions Related to perimeter and area of rectilinear figures

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

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

  1. $168{m}^{2}$

  2. $336{m}^{2}$

  3. $372{m}^{2}$

  4. $480{m}^{2}$

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Correct Option: A
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

The area of the parallelogram with diagonals $5cm, 6cm$ respectivelu

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

  1. $18cm^2$

  2. $27cm^2$

  3. $15cm^2$

  4. $None\ of\ these$

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Correct Option: C
Explanation:

The diagonals of parallelogram is $5cm,6cm$

The area of parallelogram is $\dfrac 12d _1\times d _2\\dfrac 12\times 5\times 6=15cm^2$

Point $A(2,1),B(3,-7),C$ is any point on the line $3x-2y=1$, then locus of point $D$ such that$ABCD$ is a parallelogram

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

  1. $3x-2y=20$

  2. $3x-y=20$

  3. $2x+3y=20$

  4. $3x-2y+18=0$

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Correct Option: A

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.

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

  1. $32\ m$

  2. $9\ m$

  3. $3\ m$

  4. $5\ m$

  5. $None\ of\ these$

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Correct Option: A
Explanation:
formula,

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

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

$(12.5+7.5)h=640$

$20h=640$

$\therefore h=32m$

if $\hat { i } +2\hat { j } +3\hat { k } $ and $ 3\hat { i } -2\hat { j } +\hat { k } $ are the adjacent sides of a parallelogram, then its area will be 

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

  1. $8\sqrt { 3 } $

  2. $5\sqrt { 3 } $

  3. $16\sqrt { 3 } $

  4. $6\sqrt { 3 } $

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Correct Option: A
Explanation:

We have,

$ \overrightarrow{a}=\widehat{i}+2\widehat{j}+3\widehat{k} $

$ \overrightarrow{b}=3\widehat{i}-2\widehat{j}+\widehat{k} $


We know that,

Area of parallelogram $=\left| \begin{matrix} i & j & k \\ 1 & 2 & 3 \\ 3 & -2 & 1 \end{matrix} \right| $

$ =\left( -6-2 \right)\widehat{i}-\widehat{j}\left( 9-1 \right)+\widehat{k}\left( 6+2 \right) $

$ =-8\widehat{i}-8\widehat{j}+8\widehat{k} $


$ Now, $

$ \left| \overrightarrow{a}\times \overrightarrow{b} \right|=\sqrt{{{\left( -8 \right)}^{2}}+{{\left( -8 \right)}^{2}}+{{8}^{2}}} $

$ =\sqrt{64+64+64} $

$ =\sqrt{3\times 64} $

$ =8\sqrt{3}\,\,sq.\,unit $


Hence, this is the answer.

ABCD is a parallelogram with sides $AB = 12\ cm$, $BC = 10\ cm$ and diagonal $AC = 16\ cm$. Find the approximate area of the parallelogram.

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

  1. $119.8cm^2$

  2. $103.7cm^2$

  3. $15.7cm^2$

  4. None of these

Show answer
Correct Option: A
Explanation:
Area of triangle with sides $12\ cm, 10\ cm, 16\ cm$:
$s=\dfrac{12+10+16}{2}=19$

Area, A = $\sqrt{s(s-a)(s-b)(s-c)}$

$A=\sqrt{19(19-12)(19-10)(19-16)}$

$A=59.9$ sq. cm

Therefore,
Area of parallelogram $=2A = 2\times 59.9 = 119.8$ sq. cm

Which of the following statements are true (T) and which are false (F)?
If three angles of a quadrilateral are equal, it is a parallelogram.

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

  1. True

  2. False

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Correct Option: B

Which of the following statements are true (T) and which are false (F)?
If three sides of a quadrilateral are equal, it is a parallelogram.

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

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  We know that, in parallelogram opposite sides are parallel and equal in length.

$\Rightarrow$  In some case all four sides are equal in length. ( Square and rhombus )
$\Rightarrow$  But we can't say that, three sides are equal than that is a parallelogram. That doesn't satisfied the properties of a parallelogram.
$\therefore$  If three sides of a quadrilateral are equal then it is not a parallelogram.
$\therefore$  The given statement is false.
 

Two opposite angles of a parallelogram are $(3x-2)^{\circ}$ and $(50-x)^{\circ}$. Find the measure of each angle of the parallelogram.

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

  1. $40^{\circ},140^{\circ},40^{\circ},140^{\circ}$

  2. $37^{\circ},143^{\circ},37^{\circ},143^{\circ}$

  3. $35^{\circ},145^{\circ},35^{\circ},145^{\circ}$

  4. None of these

Show answer
Correct Option: B
Explanation:

Since opposite angles of a parallelogram are equal. Therefore,
$3x-2=50-x\Rightarrow x=13$


$(3x−2)^{\circ}=3(13)-2=37^{\circ}$

The measures of the adjacent angles of a parallelogram add up to be $180$ degrees, or they are supplementary.
Another angle $=180-37=143^{\circ}$

The measure of each angle of the parallelogram.
$37^{\circ},143^{\circ},37^{\circ},143^{\circ}$

Find the measure of all the angles of a parallelogram, if one angle is $24^{\circ}$ less than twice the smallest angle.

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

  1. $68^{\circ},112^{\circ},68^{\circ},112^{\circ}$

  2. $48^{\circ},72^{\circ},48^{\circ},72^{\circ}$

  3. Insufficient data 

  4. None of these

Show answer
Correct Option: A
Explanation:

Let the smallest angle be of $x^{\circ}$. 


Then, the other angle is of $(2x-24)^{\circ}$. 

Since adjacent angles of a parallelogram are supplementary.

$\therefore x^{\circ}+(2x-24)^{\circ}=180^{\circ}\Rightarrow x=68^{\circ}$


$(2x-24)^{\circ}=2(68)-24=112^{\circ}$


The measure of all the angles of a parallelogram are
$68^{\circ},112^{\circ},68^{\circ},112^{\circ}$