Mathematics

Parallelogram Properties and Area

93 Questions

Parallelogram properties and area questions test the ability to calculate dimensions using base and height ratios. Problems also cover diagonal properties and internal angles. These geometry concepts regularly appear in quantitative aptitude sections of various exams.

Area calculationBase and height ratiosDiagonal propertiesInterior anglesGeometric theorems

Parallelogram Properties and Area Questions

Multiple choice general knowledge math & puzzles

A parallelogram has four sides and four congruent angles

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

A parallelogram has four sides, but the angles are not necessarily congruent. Only in a rectangle (a special type of parallelogram) are all angles equal to 90 degrees. In a general parallelogram, opposite angles are equal, but adjacent angles are supplementary, not congruent. Therefore, the statement is false.

Multiple choice technology databases

If the number of leaf blocks of index , scanned is less than 5000 then degree of parallelismis 2?

  1. True

  2. False
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Parallel degree depends on many factors beyond just leaf block count: system configuration, optimizer cost calculations, table size, and available CPU resources. A fixed rule of 5000 blocks = degree 2 doesn't exist. The parallel degree is determined by the optimizer based on total cost, not just block count.

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

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