Tag: maths

Questions Related to maths

If we have to construct a square $PQRS$ whose diagonal is $8 \sqrt 2$ cm then its side is equal to ?

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

  1. $8$ cm

  2. $4\sqrt2$ cm

  3. $4$ cm

  4. $8\sqrt2$ cm

Show answer
Correct Option: A
Explanation:

If the diagonal of square is $a$, then its side $=\dfrac{a}{\sqrt2}$

If diagonal is $8\sqrt2 $ cm, then its side $=\dfrac{8\sqrt2}{\sqrt2}=8$ cm.

State the following statement is True or False
The side of a square is $\sqrt2$ times the diagonal of a square

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

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

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

State the following statement is True or False
We cannot construct the square if only diagonal is given

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

  1. True

  2. False

Show answer
Correct Option: B
Explanation:

If $a$ is the diagonal of square then its side $=\dfrac{a}{\sqrt2}$

We can construct a square, with its side given.

Which of the following statements is true for a rhombus?

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

  1. It has only two pair of equal sides.

  2. Two of its angles are at right angles.

  3. Its diagonals bisect each other at right angles.

  4. It is always a square.

Show answer
Correct Option: C
Explanation:

Rhombus is a flat shape with 4 equal straight sides.All sides have equal length.Opposite sides are parallel, and opposite angles are equal.The altitude is the distance at right angles to two sides.And the diagonals "p" and "q" of a rhombus bisect each other at right angles.
So (C) is correct.
Answer (C) Its diagonals bisect each other at right angles.

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

Show answer
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) $

Show answer
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} $

Show answer
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. $\angle COD$

Show answer
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

Show answer
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.