Tag: construction of special quadrilaterals

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Questions Related to construction of special quadrilaterals

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.

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

We can construct a parallelogram if:

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

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

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.

  1. $240$
  2. $235$
  3. $270$

  4. None of these
Reveal answer Fill a bubble to check yourself
A Correct answer
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. 

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

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.

  1. $21.5$
  2. $14.5$
  3. $17.5$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
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.

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

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

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
A Correct answer
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 $b$.

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

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

  1. $2,4,3,1$
  2. $2,3,4,1$
  3. $3,2,4,1$
  4. $3,4,2,1$
Reveal answer Fill a bubble to check yourself
B Correct answer
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 $2,3,4,1$.

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

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.

  1. $(17, 12)$
  2. $(17, 5)$
  3. $(14, 16)$
  4. $(15, 3)$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

Given A(0, yA) and B(xB, 0), and D(12, 17). Since it is a square, the vector AB must be perpendicular to AD and equal in length. Solving for the coordinates of the vertices based on the square properties leads to C(17, 12).