Question

The base and height of Triangle A are half the base and the height of Triangle B. How many times greater is the area of Triangle B?

Answer 1

It would be have as great

Answer 2

$\bf \textit{area of triangle \underline{b}}\\\\ A_b=\cfrac{1}{2}bh\implies A_b=\boxed{\cfrac{bh}{2}} \\\\\\ \textit{area of triangle \underline{a}}\\\\ \begin{cases} b=\frac{b}{2}\\\\ h=\frac{h}{2} \end{cases}\implies A_a=\cfrac{1}{2}\left( \cfrac{b}{2} \right)\left( \cfrac{h}{2} \right)\implies A_a=\boxed{\cfrac{bh}{2}}\cdot \cfrac{1}{4} \\\\\\ A_a=A_b\cdot \cfrac{1}{4}\impliedby A_a\textit{ is one-quarter of }A_b$