Tag: construction of polygons

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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

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).

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 distance between AD and BC.

  1. $25 $ cm
  2. $15 $ cm
  3. $13 $ cm

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

The distance between AB and DC is the height (DE).
Area of the parallelogram ABCD = base x height = $24\times 10$ = $240$ sq cm
This is also the area of the same parallelogram with AD as the base and AH as the height.
height= $13$ width= $15$
Area of ABCD = ADx AH = $16 \times AH$
But area = $240$sqcm
I.e. AH = $\dfrac{240}{16} = 15$ cm