Question

PQRS is a parallelogram whose adjacent sides PQ=20 cm and QR= 21 cm one. of its diagonals PQ=13 cm , find
I) The area of the parallelogram PQRS.
II) The distance between the longer sides.
iii) The distance between the shorter sides.

Answer 1

see the pic
I suppose you meant the diagonal was PR instead of PQ

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Answer 2

Area of parallelogram is 252 $cm^{2}$, distance between the longer sides is 24 cm and the distance between the shorter side is 24 cm.

Step-by-step explanation:

Using heron's formula,

Diagonal SQ = 13 cm

              ⇒    s = $\frac{Perimeter of PSQ}{2}$$\frac{\textrm{peremeter of PSQ}}{2}$

              ⇒    s = $\frac{54}{2}$ = 27 cm

              ⇒      Area = $\sqrt{27(27 - 21)(27 - 20)(27 - 13)}$

               ⇒ Area = 126 $cm^{2}$

Area of parallelogram,

                  ⇒ Area = 252 $cm^{2}$

           For distance,

                      ⇒ 126 = 0.5 x 21 x h

So, distance between the shorter sides is,

                       ⇒ h = 25.2 cm

                         

 Now,

                     ⇒ 126 = 0.5 x 20 x h

So, distance between the longer distances,

                      ⇒ h = 24 cm