Tag: construction of polygons

Questions Related to construction of polygons

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

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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. 

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.

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

  1. $21.5$

  2. $14.5$

  3. $17.5$

  4. None of these

Show answer
Correct Option: C
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.

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

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:

Length diagonal having sides $a$ and $b$ $=\sqrt{a^2+b^2}$ 

Which is greater than any of its side that is $a$ and $b$.

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

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

  1. $2,4,3,1$

  2. $2,3,4,1$

  3. $3,2,4,1$

  4. $3,4,2,1$

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Correct Option: B
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 $2,3,4,1$.

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.

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

  1. $(17, 12)$

  2. $(17, 5)$

  3. $(14, 16)$

  4. $(15, 3)$

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Correct Option: A

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.

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

  1. $25 $ cm

  2. $15 $ cm

  3. $13 $ cm

  4. None of these

Show answer
Correct Option: B
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