Tag: maths

Questions Related to maths

A parallelogram has an area of $60$ $cm^{2}$ and a base of $12$ cm. Find the height.

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

  1. $3$ cm

  2. $4$ cm

  3. $5$ cm

  4. $6$ cm

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Correct Option: C
Explanation:

Area of a parallelogram = base $\times$ height
$60 = 12 \times height$
height = $60 \div 12$
height = $5$ cm

Find the area of a parallelogram with a base of $34$ meters and a height of $8$ meters.

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

  1. 262 $m^{2}$

  2. 272 $m^{2}$

  3. 282 $m^{2}$

  4. 292 $m^{2}$

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Correct Option: B
Explanation:

Area of a parallelogram = base $\times$ height
= $34 \times 8$
= $272$ $m^{2}$

A parallelogram has an area of $125$ $m^{2}$ and a height of $5\ m.$ Find the base.

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

  1. $250$ m

  2. $25$ m

  3. $270$ m

  4. $28$ m

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Correct Option: B
Explanation:

Area of a parallelogram$=base\times height$. Let the base be 'b'.
Hence
$125m^{2}=5b$ or $b=25m$
Therefore $base=25m$.

Find the base of parallelogram if its area is $\displaystyle 80{ cm }^{ 2 }$ and altitude is $10$ cm.

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

  1. $6$ cm

  2. $8$ cm

  3. $10$ cm

  4. None of the above

Show answer
Correct Option: B
Explanation:

Area of parallelogram $\displaystyle =b\times a$
$\displaystyle 80=b\times 10$
$\displaystyle b=8cm$


So, option B is correct.

Find the area of a parallelogram with a base of $200$ cm and height of $2.5$ cm.

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

  1. $500$ $cm^{2}$

  2. $510$ $cm^{2}$

  3. $520$ $cm^{2}$

  4. $300$ $cm^{2}$

Show answer
Correct Option: A
Explanation:

Area of a parallelogram = base $\times$ height
= $200 \times 2.5$
= $500$ $cm^{2}$

Calculate the area of a parallelogram with a base of $ 12$ m and height of $5$ m.

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

  1. 59 $m^{2}$

  2. 60 $m^{2}$

  3. 61 $m^{2}$

  4. 62 $m^{2}$

Show answer
Correct Option: B
Explanation:

Area of a parallelogram = base $\times$ height
= $12 \times 5$
= $60$ $m^{2}$

The base and the corresponding altitude of a parallelogram are $10: cm$ and $3.5: cm$, respectively. The area of the parallelogram is

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

  1. $30: cm^2$

  2. $35: cm^2$

  3. $70: cm^2$

  4. $ 17.5:cm^2$

Show answer
Correct Option: B
Explanation:

The area of the parallelogram is base $\times$ height $cm^2$

Area of the parallelogram$=(10)(3.5)=35:cm^2$.

If the base of a parallelogram is $8\ cm$ and its altitude is $5\ cm$, then its area is equal to

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

  1. $15\ cm^{2}$

  2. $20\ cm^{2}$

  3. $40\ cm^{2}$

  4. $10\ cm^{2}$

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Correct Option: C
Explanation:

Area of parallelogram $=Base \times height $

$=8\times 5\ =40\ { cm }^{ 2 }$

A parallelogram has sides $30 m, 70 m$ and one of its diagonals is $80 m$ long. Its area will be

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

  1. $600\displaystyle m^{2}$

  2. $\displaystyle 1200\sqrt{3}m^{2}$

  3. $1200\displaystyle m^{2}$

  4. $\displaystyle 600\sqrt{3} m^{2}$

Show answer
Correct Option: B
Explanation:
The diagonal of parallelogram divides it into two congruent triangles. 
$\therefore $ Area (parallelogram $ABCD) = 2 \times$ Area $ \left (\Delta ABC  \right ) $
In $ \Delta ABC$,
$ s=\cfrac{80m+ 30m+70m}{2}=\cfrac{180m}{2}=90m$
$ \therefore Area=\sqrt{90\left ( 90-80 \right )(90-30)(90-70)}m^{2}$
$ =\sqrt{90\times10\times60\times20m^{2} }$
$= 600\sqrt{3} m^{2}$

$ \therefore $ Area of parallelogram $ABCD =$$ 2\times 600\sqrt{3}m^{2}$ $ =1200\sqrt{3}m^{2}$

The value of $a$ for which the function $f(x)=a\ \sin x+\dfrac{1}{3}\sin 3x$ has an extremum at $x=\dfrac{\pi}{3}$ is

maths application of derivatives - iii second derivative test maxima and minima application of derivatives

  1. $1$

  2. $-1$

  3. $0$

  4. $2$

Show answer
Correct Option: D
Explanation:
$f\left( x \right) = a\sin x + \dfrac{1}{3}\sin 3x$
$ \Rightarrow f'\left( x \right) = a\cos x + \dfrac{1}{3}\cos 3x \times 3$
$ \Rightarrow f'\left( x \right) = a\cos x + \cos 3x$
For extremum at ${\dfrac{\pi }{3}}$
$f'\left( {\dfrac{\pi }{3}} \right) = 0$
$ \Rightarrow a\cos \left( {\dfrac{\pi }{3}} \right) + \cos 3\left( {\dfrac{\pi }{3}} \right) = 0$
$ \Rightarrow \dfrac{a}{2} - 1 = 0$
$\Rightarrow a = 2$