Question

In the below diagram, ABCD is rectangle with AE = EF = FB. What is the ratio of the areas of $\Delta CEF$ and that of the rectangle?

• A. $\frac{1}{6}$
• B. $\frac{1}{8}$
• C. $\frac{1}{9}$
• D. None of these

Answer 1

The correct option is A $\frac{1}{6}$

Area of triangle $\Delta CEF=$ area of $\Delta CEB-$ area of $\Delta CFB$

$=\frac{1}{2}EB\times BC-\frac{1}{2}FB\times BC$

$=\frac{1}{2}\left(\frac{2AB}{3}\right)\times BC-\frac{1}{2}\left(\frac{2AB}{3}\right)\times BC$

$=\frac{1}{6}\times AB\times BC$

Area of rectangle $=AB\times BC$

$\frac{\text{area of triangle}}{\text{area of rectangle}}=\frac{\frac{1}{6}\times AB\times BC}{AB\times BC}=\frac{1}{6}$