Question

$△$ADC is formed by joining the coordinates A(2,6), C(4,0) and D(0,0). Another $△$BCD is formed by joining the coordinates B(6,6), C(4,0) and D(0,0). BD intersects AC at O. What is the relation between the areas of $△$AOD and $△$BOC?

• A. True
• B. False
• C. Area of $△$AOD = $\frac{1}{4}$ Area of $△$BOC
• D. $\frac{1}{2}$ Area of $△$AOD = Area of $△$BOC

Answer 1

The correct option is A

True

AB is joined. Since y = 6 and y = 0 are parallel to each other; AD and BC are parallel to each other.
And, triangles between the same base and same parallels have equal area.
Thus, Area of$\Delta$ADC = Area of $\Delta$BDC
$\Rightarrow$Area of$\Delta$ADC - Area of $\Delta$DOC = Area of $\Delta$BDC - Area of $\Delta$DOC
$\Rightarrow$ Area of $\Delta$AOD = Area of $\Delta$BOC.

Hence, the statement is correct.