Problem C

A Bigger Triangle

Naveen drew a right-angled triangle, \(\triangle ABC\), with an area of \(14~\text{cm}^2\). His brother Anand drew a bigger right-angled triangle, \(\triangle DEF\), with side lengths four times the lengths of the sides in \(\triangle ABC\). In particular, \(DE=4\times AB\), \(EF=4\times BC\), and \(DF=4\times AC\).

Calculate the area of \(\triangle DEF\).

**Theme: **Geometry & Measurement