Tag: construction of parallelograms and rectangles

Questions Related to construction of parallelograms and rectangles

What would be the length of side $BC$ in Square $ABCD$ if the diagonal of the square given is $10$ cm?

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. $5$ cm

  2. $5\sqrt2$ cm

  3. $10$ cm

  4. $10\sqrt2$ cm

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Correct Option: B
Explanation:

The side of a square is $\dfrac{1}{\sqrt2}$ times of the diagonal.


If the length of diagonal $=10$ cm

Then length of side $=10\times \dfrac{1}{\sqrt2}=5\sqrt2$ cm.

If one diagonal of a square is the portion of the line $\frac { x }{ a } +\frac { y }{ b } =1$ intercepted by the axes, then the extremities of the other diagonal of the square are

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. $\left( \frac { a+b }{ 2 } ,\frac { a+b }{ 2 } \right) $

  2. $\left( \frac { a-b }{ 2 } ,\frac { a+b }{ 2 } \right) $

  3. $\left( \frac { a-b }{ 2 } ,\frac { b-a }{ 2 } \right) $

  4. $\left( \frac { a+b }{ 2 } ,\frac { b-a }{ 2 } \right) $

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Correct Option: C

The side of a regular hexagon is 'p' cm then its area is

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. $ \displaystyle \frac{\sqrt{3}}{2}p^{2}cm^{2} $

  2. $ \displaystyle \frac{3\sqrt{3}}{2}p^{2}cm^{2} $

  3. $ \displaystyle 2\sqrt{3}p^{2}cm^{2} $

  4. $ \displaystyle 6p^{2}cm^{2} $

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Correct Option: B
Explanation:

Given side of hexa gon is p cm 

Then area of hexagon =$\frac{(side)^{2}\times  n}{4tan\frac{180}{n}}=\frac{p^{2}\times 6}{4tan\frac{180}{6}}=\frac{6p^{2}}{4tan30^{0}}=\frac{3p^{2}}{2\times \frac{1}{\sqrt{3}}}=\frac{3\sqrt{3}p^{2}}{2} cm^{2}$

The diagonal of rectangle $ABCD$ intersect each other at $O$. If $\angle AOB = 30^0$, then we can construct a rectangle if _________ is given.

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. diagonal

  2. one side

  3. both sides

  4. $\angle COD$

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Correct Option: A,C
Explanation:

$ABCD$ is a rectangle

$\implies AB = CD$ and $AD = BC$ ... (1)
By knowing these, we can just draw the two pair of parallel lines but the length is not fixed.
So, to  draw a rectangle we need the length of the sides.
From (1), we need only the length of two adjacent sides.
Hence, we can construct a rectangle if both sides are given.

We can construct a parallelogram if:

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. its adjacent sides and a diagonal are given

  2. its diagonal and one angle are given

  3. its four angles and a side are given

  4. None of these are given

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Correct Option: A
Explanation:

Steps to create a parallelogram($ABCD$),

$(i)$ Draw one line segment of length $AB$.
$(ii)$ Make an arc of length $BC$ from $B$ and an arc of length $AC$ from $A$.
$(iii)$ Name the intersection point of both the arcs as $C$. Join $A-C$ and $B-C$.
$(iv)$ After completing this process we get $2$ adjacent sides and one diagonal of a parallelogram $ABCD$.
$(v)$ Since, opposite sides are equal and parallel in a parallelogram. So, draw an arc of length $AB$ from $C$ and an arc of length $BC$ from $A$ and name the intersection point as $D$.
$(vi)$) And then join $C-D$ and $A-D$.
At-last we get a parallelogram $ABCD$.
To construct $ABCD$, we need $2$ adjacent sides $AB$ and $BC$ and length of diagonal $AC$.
By knowing only these $3$ parameters we can construct a parallelogram.
Hence, option A is correct.

Construct a parallelogram $ABCD$ with $AB=24$ cm and $AD=16$ cm. The distance between AB and DC is $10$ cm. Find the area of parallelogram $ABCD$ in sq. cm.

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. $240$

  2. $235$

  3. $270$

  4. None of these

Show answer
Correct Option: A
Explanation:

Area of parallelogram ABCD

$=AB\times \left( altitude\quad associated\quad with\quad AB \right) \ =24\times 10\ =240 sq. cm$
So, correct answer is option A. 

Construct a parallelogram $ABCD$, with adjacent sides $AB=4$ cm, $BC = 5$ cm and height corresponding to  (base) $BC = 3.5$ cm. Find the area of parallelogram ABCD in sq. cm.

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. $21.5$

  2. $14.5$

  3. $17.5$

  4. None of these

Show answer
Correct Option: C
Explanation:

Area of parallelogram ABCD

$=BC\times \left( altitude\quad associated\quad with\quad BC \right) \ =5\times 3.5\ =17.5$
So, correct answer is option C.

State whether the following statement is True or False.
The length of diagonal of rectangle is more than any side of rectangle.

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. True

  2. False

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Correct Option: A
Explanation:

Length diagonal having sides $a$ and $b$ $=\sqrt{a^2+b^2}$ 

Which is greater than any of its side that is $a$ and $b$.

Construct a rectangle $ABCD$, where $AB=10$ cm and $BC=8$ cm.Steps for its construction is given in a jumbled form. Identify its correct sequence.
1) Join these cuts with a line $CD$ and rectangle $ABCD$ is formed
2) Draw a straight line $AB$ of length $10$ cm
3) Draw perpendicular lines at $A$ and $B$ using protractor.
4) Using compass cut arc at the perpendicular from $A$ and $B$ of lengths $8$ cm

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. $2,4,3,1$

  2. $2,3,4,1$

  3. $3,2,4,1$

  4. $3,4,2,1$

Show answer
Correct Option: B
Explanation:

Correct sequence for constructing rectangle $ABCD$ is:

Draw a straight line $AB$ of $10 $ cm.
Draw perpendicular lines at $A$ and $B$ using proctor.
Using compass cut arc at the perpendicular from $A$ and $B$ of lengths $8$ cm.
Join these cuts with a line $CD$ and rectangle $ABCD$ is formed.
Correct sequence is $2,3,4,1$.

Let $ABCD$ be a square in which $A$ lies on the positive y-axis and $B$ lies on the positive x-axis. If $D$ is the point $(12, 17)$ the coordinates of $C$ are.

maths construction of polygons construction of parallelograms and rectangles construction of special quadrilaterals constructions related to a quadrilateral

  1. $(17, 12)$

  2. $(17, 5)$

  3. $(14, 16)$

  4. $(15, 3)$

Show answer
Correct Option: A