Question

Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O.Then

• A. Area of $\Delta$ AOD $=\left(\frac{1}{2}\right)$ Area of $\Delta$ BOC
• B. Area of $\Delta$ AOD$=\left(\frac{1}{2}\right)$ Area of $\Delta$ BOC
• C. Area of $\Delta$ AOD =Area of $\Delta$ BOC
• D. None of these

Answer 1

The correct option is C Area of $\Delta$ AOD =Area of $\Delta$ BOC

Triangles on the same base and between same parallels are equal in area.

Hence, Area of $\Delta$ ADC = Area of $\Delta$ BDC
$\Rightarrow$ Area of $\Delta$ AOD + Area of $\Delta$ DOC
= Area of $\Delta$ BOC + Area of $\Delta$ DOC
$\Rightarrow$ Area of $\Delta$ AOD = Area of $\Delta$ BOC