In the given figure, ABCDE is a pentagon with AC = 5 cm. A line through B parall

Question

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

Options:

A . 5 cm2

B . 10 cm2

C . 15 cm2

D . 30 cm2

Answer: Option C
:
C

Let BG be perpendicular to AC.
Fromthe given figure:
AC

∥

BF (given)
AC = 5cm (given)
Length of the altitude BG, perpendicular to AC = 6 cm (given)

△ A C B and △ A C F lie on the same base ACand are between the same parallels ACand BF.

∴ Area △ A C B = Area △ A C F

Area △ A C B = \frac{1}{2} \times base \times Height = \frac{1}{2} \times 5 \times 6 = 15 c m^{2}

∴ Area △ A C F = 15 c m^{2}

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