Question

Forth grade math: What happens to the area of the triangle when one of the dimensions is doubled and halved?

Answer 1

$\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ b=\stackrel{doubled}{2b} \end{cases}\implies A=\cfrac{1}{2}(2b)(h)\implies \stackrel{\textit{twice as the original area}}{A=bh} \\\\[-0.35em] ~\dotfill$

$\bf \textit{area of a triangle}\\\\ A=\cfrac{1}{2}bh~~ \begin{cases} b=base\\ h=height\\[-0.5em] \hrulefill\\ h=\stackrel{halved}{\frac{h}{2}} \end{cases}\implies A=\cfrac{1}{2}b\left( \cfrac{h}{2} \right)\implies \stackrel{\textit{half of the original area}}{A=\cfrac{1}{2}bh\left( \cfrac{1}{2} \right)}$