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 triangle ADF = (1/2) × Area of triangle BEC
• B. Area of triangle ADF = 1 × Area of triangle BEC
• C. Area of triangle ADF = (1/4) × Area of triangle BEC
• D. Area of triangle ADF = 2×Area of triangle BEC

Answer 1

The correct option is B

Area of triangle ADF = 1 × Area of triangle BEC

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 quad ABOD = Area of quad AOEB
$\Rightarrow$ 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