Question

PQ is a line parallel to side BC and passing through vertex A of a triangle ABC. If BE || AC and CF || AB meet PQ at E and F, respectively. If the base and altitude of ΔABC are 6 cm and 8 cm, respectively, then find the area of ΔACF.

• A. 12 $c{m}^2$
• B. 24 $c{m}^2$
• C. 48 $c{m}^2$
• D. 54 $c{m}^2$

Answer 1

The correct option is B 24 $c{m}^2$

CF when drawn parallel to AB, forms parallelogram ABCF.

AC is the diagonal of the parallelogram that divides ABCF into 2 equal triangles ABC and ACF.

So, Area of ΔACF = Area of ΔABC = $\frac{1}{2}\times 6\times 8=24c{m}^2$