Tag: construction of parallelograms and rectangles

Questions Related to construction of parallelograms and rectangles

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