Question

In the adjoining figure, a trapezium ABCD is shown in which AB || DC then, ar (ΔAOD) is equal to:

Options

• ar (ΔOCD)

• ar (ΔAOB)

• ar (ΔBCD)

• ar (ΔBOC)

Answer 1

ar (ΔBOC)

Explanation:

With AB || DC, the triangles AOB and COD are similar, alternate interior angles and vertical angles. 

So, `(AO)/(OC) = (BO)/(OD)`.

The area of ΔAOD = `1/2` × AO × OD × sin θ and the area of ΔBOC = `1/2` × BO × OC × sin θ, where θ is the vertical angle between the two diagonal segments.

Hence, `("area" (AOD))/("area" (BOC))` 

= `(AO xx OD)/(BO xx OC)` 

= 1

So, area (AOD) = area (BOC).