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.
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