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 $△$ABC (perpendicular to AC) is 6 cm.The area of $△$AFC is _____.

• A. 5 cm²
• B. 10 cm²
• C. 15 cm²
• D. 30 cm²

Answer 1

The correct option is C

15 cm²

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

$\therefore \text{Area}\left(△ACB\right)=\text{Area}\left(△ACF\right)\text{Area}\left(△ACB\right)=\frac{1}{2}\times \text{base}\times \text{Height}=\frac{1}{2}\times 5\times 6=15c{m}^2$