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 C

Let ABCDE be a pentagon. We have to construct a triangle of area equal to the area of ABCDE and one of whose vertices is C.
Method of Construction:
(1) Let us 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 which intersects BF at Q
(6) C, P and C, Q are joined.
Then, $\Delta PCQ$ is the required triangle to be constructed.
$\therefore$ Area of $\Delta PCQ$ = Area of pentagon ABCDE.