Question

Draw a pentagon ABCDE and construct a triangle equal in area to the

pentagon​

Answer 1

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.

ΔPCQ is the required triangle to be constructed.

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