Question

Points A(1,0), B(5,0), C(7,6) and D(3,6) are joined to form a quadrilateral ABCD. Point B(5,0) is joined with E(5,6); and A(1,0) is joined with F(1,6). Quadrilateral ABEF is completed. BD and AE is joined to intersect at O. Which of the following is correct?

• A. Area of ABODF = (1/2) × Area of BAOEC
• B. Area of ABODF = 1×Area of BAOEC
• C. Area of ABODF = (1/4) × Area of BAOEC
• D. Area of ABODF = 2 × Area of BAOEC

Answer 1

The correct option is B

Area of ABODF = 1×Area of BAOEC

Figures on the same base and between the same parallels have equal area. Quad ABCD forms a parallelogram; and Quad ABEF forms a rectangle.
Both the figures are on the same base AB and between the same parallels AB and CF.

Thus area of quad ABCD = Area of quad ABEF; and Area of $\Delta$ABD = Area of $\Delta$AEB.
$\Rightarrow$ Area of quad ABCD - Area of quad ABED = Area of quad ABEF - Area of quad ABED
$\Rightarrow$ Area of $\Delta$ADF = Area of $\Delta$BEC.

Hence, Area of $\Delta$ABD + Area of $\Delta$ADF = Area of $\Delta$AEB + Area of $\Delta$BEC
$\Rightarrow$ Area of figure ABODF = Area of figure BAOEC.

Area of figure ABODF = 1$\times$Area of figure BAOEC.