Question

In the adjoining figure, MNPQ and ABPQ are parallelograms and T is any point on the side BP. Prove that

(i) ar (MNPQ) = ar (ABPQ)

(ii) ar (△ ATQ) = ½ ar (MNPQ).

Answer 1

(i) From the figure we know that the parallelograms MNPQ and ABPQ are on the same base PQ and lie between the same parallels PQ and MB.

So we get

Area of parallelogram MNPQ = Area of parallelogram ABPQ

Therefore, it is proved that ar (MNPQ) = ar (ABPQ).

(ii) From the figure we know that △ ATQ and parallelogram ABPQ lie on the same base AQ and between the same parallels AQ and BP.

So we get

Area of △ ATQ = ½ (Area of parallelogram ABPQ)

It can be written as

Area of △ ATQ = ½ (Area of parallelogram MNPQ)

Therefore, it is proved that ar (△ ATQ) = ½ ar (MNPQ).