Question

In the adjoining figure, a parallelogram ABCD is shown. If DM ⊥ AB, DN ⊥ BC, then area of ΔABD is equal to:

Options

• `1/2 xx AB xx DN`

• `1/2 xx BC xx DN`

• `1/2 xx BC xx DM`

• `1/2 xx AD xx DM`

Answer 1

`bb(1/2 xx BC xx DN)`

Explanation:

Diagonal BD splits parallelogram ABCD into two equal-area triangles.

So, area (△ABD) = area (△CBD).

In △CBD, the base is BC and the height from D to BC is DN (given DN ⟂ BC).

So, area = `1/2` × BC × DN.