Question

Two similar hexagons have corresponding heights of 3 m and 4 m. If the area of the smaller hexagon is 13 m2, what is the area of the larger hexagon? (Round your answer to one decimal place.)

Answer 1

$\bf \qquad \qquad \textit{ratio relations} \\\\ \begin{array}{ccccllll} &Sides&Area&Volume\\ &-----&-----&-----\\ \cfrac{\textit{similar shape}}{\textit{similar shape}}&\cfrac{s}{s}&\cfrac{s^2}{s^2}&\cfrac{s^3}{s^3} \end{array} \\\\ -----------------------------$

$\bf \cfrac{\textit{similar shape}}{\textit{similar shape}}\qquad \cfrac{s}{s}=\cfrac{\sqrt{s^2}}{\sqrt{s^2}}=\cfrac{\sqrt[3]{s^3}}{\sqrt[3]{s^3}}\\\\ -------------------------------\\\\ \cfrac{smaller}{larger}\qquad \cfrac{3}{4}=\cfrac{\sqrt{13}}{\sqrt{a}}\implies \cfrac{3}{4}=\sqrt{\cfrac{13}{a}}\implies \left( \cfrac{3}{4} \right)^2=\cfrac{13}{a} \\\\\\ \cfrac{3^2}{4^2}=\cfrac{13}{a}\implies \cfrac{9}{16}=\cfrac{13}{a}\implies a=\cfrac{16\cdot 3}{9}$