Question

Construct any pentagon ABCDE and then construct a triangle (PCQ) of area equal to the area of ABCDE and one of whose vertices in C. Which of the following is the correct diagram for the triangle PCQ?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let ABCDE be a pentagon. We need to construct a triangle of area equal to the area of ABCDE and one of whose vertices is C.

Method of Construction:
(1) Draw the diagonals CE and CA of the pentagon ABCDE.
(2) Draw DG through D parallel to CE.
(3) Draw BF through B parallel to CA.
(4) Produce AE (on the left side), which intersects DG at P.
(5) Produce EA (on right side) which intersects BF at Q.
(6) C, P, C, Q are to be joined.
$\Delta PCQ$ is the required triangle to be constructed.