Question

In the given figure, AB is parallel to DС and AB ≠ DC, the area of ΔAOD is equal to area of triangle:

Options

• AOB

• COD

• ACB

• BOC

Answer 1

BOC

Explanation:

In trapezium ABCD, the sides AB and DC are parallel. Triangles ΔABC and ΔABD share the same base AB and lie between the same parallel lines AB and DC, which means their total areas are equal:

area of ΔABC = area of ΔABD

Subtracting the common triangle ΔAOB from both sides:

area of ΔABC − area of ΔAOB = area of ΔABD − area of ΔAOB

area of ΔBOC = area of ΔAOD

Thus, the area of ΔAOD is equal to the area of ΔBOC.