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In how many parts the fields is divided? What are the shapes of these parts?

The farmer wants to sow wheat and pulses in equal portions of the field separately.

How should she do it?

Answer :

From the figure, we can say that it is that point A which divides the field into three parts.

These parts are triangular in shape i.e., \(\triangle{PSA}\), \(\triangle{PAQ}\) and \(\triangle{QRA}\)

Thus, Area \(\triangle{PSA}\) + Area \(\triangle{PAQ}\) + Area \(\triangle{QRA}\) = Area of Parallelogram PQRS ...(i)

Also, Area \(\triangle{PAQ}\) = (\(\frac{1}{2} \)) Area of Parallelogram PQRS ...(ii)

From equation (i) and (ii), we get,

Area \(\triangle{PSA}\) + Area \(\triangle{QRA}\) = \(\frac{1}{2}\) Area of Parallelogram PQRS ...(iii)

Clearly, it can be observed that the farmer must sow wheat in triangular part PAQ and pulses in other
two triangular parts PSA and QRA or wheat in triangular parts PSA and QRA and pulses in triangular parts PAQ.

- In Figure, ABCD is a parallelogram, \(AE\perp{DC}\) and \(CF\perp{AD}\). If AB = 16 cm, AE = 8 cm and CF = 10 cm, find AD.
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