Question

Points A(0,0), B(4,0), C(6,6) and D(2,6) are joined to form quadrilateral ABCD. Point C(6,6) and point B(4,0) are joined to point F(8,0). The quadrilateral DBFC is now completed. Which of the following is correct?

• A. Area of quad ABCD = (1/2) × Area of quad DBFC
• B. Area of quad ABCD = 1 × Area of quad DBFC
• C. Area of quad ABCD = (1/4) × Area of quad DBFC
• D. Area of quad ABCD = 2 × Area of quad DBFC

Answer 1

The correct option is B

Area of quad ABCD = 1 × Area of quad DBFC

ABCD is a quadrilateral with AB = CD and AB $\parallel$ CD ( A quadrilateral with opposite sides parallel and equal is a parallelogram)
DBFC is a quadrilateral with DC = BF and DC $\parallel$ BF (A quadrilateral with opposite sides parallel and equal is a parallelogram)
Thus, ABCD and DBFC are parallelograms with same base DC and in the same parallels between AF and CD.
Parallelogram in the same base and between the same parallels are equal in area.
Therefore, Area of quadrilateral ABCD = Area of quadrilateral DBFC.