Tag: perimeter and area of rectilinear figures

Questions Related to perimeter and area of rectilinear figures

If the area of a parallelogram is $144 \operatorname { cm } ^ { 2 }$ and its base is $9 cm$. then its height is 

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

  1. $8 cm$

  2. $12 cm$

  3. $24 cm$

  4. $16 cm$

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Correct Option: D
Explanation:

Area of parallelogram $=base\times height$


$\Rightarrow$ $144{cm}^{2}=9cm\times 10cm$


$\Rightarrow$ $h$ in $cm=\cfrac{144{cm}^{2}}{9cm}$

$\therefore$ $h=16cm$

Hence height $=16cm$

Area of the parallelogram formed by the pairs of lines $x^{2}+xy-^{2}=0$ and $x^{2}+xy-y^{2}-3x-4y+1=0$ is

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

  1. $\sqrt {5}$

  2. $\dfrac {1}{\sqrt {5}}$

  3. $2\sqrt {5}$

  4. $\dfrac {2}{\sqrt {5}}$

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Correct Option: C

A parallelogram has sides 12 cm and 9 cm. If the distance between its shorter sides is 8 cm, find the distance between its longer side.

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

  1. $3 \ cm$

  2. $6 \ cm$

  3. $9 \ cm$

  4. $12 \ cm$

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Correct Option: B
Explanation:

Adjacent sides of parallelogram $= 12\ cm$ and $9\ cm$

Distance between shorter sides $= 8\ cm$

Area of parallelogram = $b \times h =9 \times 8 =72 \ cm^2$

Again, area of parallelogram = $b \times h$
$72 =12 \times h$
$h= 6 \ cm$

Therefore, the distance between its longer side $= 6\ cm.$

The area of parallelogram if the base is $36cm$  and height is $45cm$

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

  1. 1620

  2. 1800

  3. 1250

  4. 1640

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Correct Option: A
Explanation:

The base of parallelogram is $36cm$

The height is $45cm$
The area of parallelogram is $36\times 45=1620cm^2$

If $ABCD$ is a parallelogram then the ratio of the areas of parallelogram $ABCD$ and $\displaystyle \Delta ABC$ is

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

  1. $1 : 2$

  2. $2 : 1$

  3. Cannot be determined

  4. None

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Correct Option: B
Explanation:

$2 : 1$
Diagonal resolves a parallelogram into two equal triangles.

Find the area of the parallelogram whose base is $17\ cm$ and height $0.8\ m$?

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

  1. $\displaystyle 13.6:cm^{2}$

  2. $\displaystyle 1360:cm^{2}$

  3. $\displaystyle 13.6:m^{2}$

  4. $\displaystyle 1360:m^{2}$

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Correct Option: B
Explanation:

Base $= 17\ cm$
Height $= 0.8\ m =0.8 \times 100 = 80\ cm$
Area of parallelogram 
$= b \times h$
$= 17\times 80$
$= 1360\ cm^2$

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:

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

  1. $7 m$

  2. $6 m$

  3. $5 m$

  4. $3 m$

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Correct Option: B
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 $= \cfrac{Area }{Base}=\cfrac{120m^{2}}{20m}=6m$

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?

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

  1. $7 : 5$

  2. $40 : 3$

  3. $15 : 2$

  4. $30 : 1$

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Correct Option: A
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 $35$.

The area of a parallelogram is $120$  $cm^{2}$ and its altitude is $10$ cm. The length of the base is

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

  1. $24$ cm

  2. $12$ cm

  3. $8$ cm

  4. $4$ cm

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Correct Option: B
Explanation:

Area of parallelogram 
= $Base \times height = 120 cm^{2}$.
$\therefore $  Base = $12 cm$

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

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

  1. 24 $cm^2$

  2. 36 $cm^2$

  3. 40 $cm^2$

  4. 48 $cm^2$

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Correct Option: D
Explanation:

As we know,

Area of Parallelogram $=bh$
Here, $b=8$ cm, $h=6$ cm
Area of Parallelogram $=8\times 6$
Area of Parallelogram $=48\ cm^2$.