Question Number 20149 by ajfour last updated on 22/Aug/17
Commented by ajfour last updated on 22/Aug/17
$${The}\:{roof}\:{is}\:{even}\:{a}\:{flat}\:{plane}.{Lengths} \\ $$$$\boldsymbol{{a}},\:\boldsymbol{{b}},\:\boldsymbol{{c}},\:\boldsymbol{{y}}\:{are}\:{perpendicular}\:{to}\:{the} \\ $$$${bottom}\:{rectangular}\:{face}\:{with}\:{sides} \\ $$$$\boldsymbol{{h}}\:{and}\:\boldsymbol{{l}}\:.\:{Find}\:{height}\:\boldsymbol{{y}}\:{and}\:{the}\:\:{volume} \\ $$$${enclosed}\:{by}\:{the}\:{surfaces}. \\ $$
Answered by mrW1 last updated on 22/Aug/17
$$\frac{\mathrm{a}+\mathrm{y}}{\mathrm{2}}=\frac{\mathrm{b}+\mathrm{c}}{\mathrm{2}} \\ $$$$\Rightarrow\mathrm{y}=\mathrm{b}+\mathrm{c}−\mathrm{a} \\ $$$$ \\ $$$$\mathrm{V}=\mathrm{l}×\mathrm{h}×\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{y}}{\mathrm{4}}=\mathrm{l}×\mathrm{h}×\frac{\mathrm{a}+\mathrm{b}+\mathrm{c}+\mathrm{b}+\mathrm{c}−\mathrm{a}}{\mathrm{4}} \\ $$$$=\frac{\mathrm{lh}\left(\mathrm{b}+\mathrm{c}\right)}{\mathrm{2}} \\ $$
Commented by ajfour last updated on 22/Aug/17
$${thank}\:{you}\:{Sir},\:{you}\:{make}\:{it}\:{so}\:{simple}! \\ $$
Answered by ajfour last updated on 23/Aug/17