Tag: construction of polygons

Quizzes (4) Questions (37)

Questions Related to construction of polygons

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

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?

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $8$ cm
  2. $4\sqrt2$ cm
  3. $4$ cm
  4. $8\sqrt2$ cm
Reveal answer Fill a bubble to check yourself
A Correct answer
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.

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

Which of the following statements is true for a rhombus?

  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.
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. $5$ cm
  2. $5\sqrt2$ cm
  3. $10$ cm
  4. $10\sqrt2$ cm
Reveal answer Fill a bubble to check yourself
B Correct answer
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.

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

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

  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) $
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

The line x/a + y/b = 1 intercepts the axes at (a, 0) and (0, b). These are the extremities of one diagonal of a square. The center of the square is the midpoint ((a/2), (b/2)). The other diagonal is perpendicular and of equal length, leading to the coordinates ((a-b)/2, (b-a)/2) for the other extremities.

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

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

  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} $
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Given side of hexa gon is p cm 

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

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

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

  1. diagonal

  2. one side

  3. both sides
  4. $\angle COD$
Reveal answer Fill a bubble to check yourself
A,C Correct answer
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.