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Question

In a pentagon ABCDE with AC = 5 cm, a line through B parallel to AC meets DC produced at F. The altitude of triangle ABC, perpendicular to AC, is 6 cm. Find the area of triangle ACF.


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Solution

Let BG be perpendicular to AC.
From the given figure:
AC BF (given)
AC = 5cm (given)
Length of the altitude BG, perpendicular to AC = 6 cm (given)

ACB and ACF lie on the same base AC and are between the same parallels AC and BF.

Area ACB = Area ACF

Area ACB=12×base ×Height= 12×5×6=15 cm2

Area ACF =15 cm2


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