Tag: construction of polygons

Questions Related to construction of polygons

When given a square, the construction of an angle bisector at any vertex will create the diagonal of the square. 

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:

This is statement is true

We know that diagonals of square bisects the angle. So angle bisector will be diagonal.

You are given the length of a diagonal of a rhombus and one of the angles of the rhombus. Which property of the rhombus will be used in the construction of this rhombus?

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

  1. The lengths of the sides of a rhombus are equal.

  2. The angles of a rhombus are $90^\circ$

  3. Diagonal of a rhombus bisects the opposite angles.

  4. Diagonals of a rhombus are perpendicular bisectors of each other.

Show answer
Correct Option: C
Explanation:

$\Rightarrow$   We have given the length of diagonal of rhombus and one of angles of rhombus.

$\Rightarrow$  To construct an rhombus we will use the property that the diagonal of a rhombus bisect the opposite angle.
Because we know opposite angles of rhombus are equal, so it will be easier to construct rhombus.

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

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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.

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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) $

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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} $

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. $\angle COD$

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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.