Question

Un trunchi de piramida triunghiulară regulats are laturile bazelor de 18 respectiv 12 cm, iar apotema de radical 15cm. Inaltimea trunchiului este egala cu…

Answer 1

$a_{b} = apotema \: \: bazei \: \: mici = \frac{\ell \sqrt{3} }{2} = 6 \sqrt{3} \\ \\ a _{B} = apotema \: \: bazei \: \: mari = \frac{\ell \sqrt{3} }{2} = 9 \sqrt{3} \\ \\ \\ \implies \: ap = apotema \: \: trunchiului \\ \iff \: ap {}^{2} = h {}^{2} + ( \tfrac{a_{B}}{3} -\tfrac{ a _{b}}{3}) {}^{2} \\ \: \sqrt{15} {}^{2} = h {}^{2} + (3 \sqrt{3} - 2 \sqrt{3} ) {}^{2} \\ \: 15 = h {}^{2} + ( \sqrt{3} ) {}^{2} \\ h {}^{2} + 3 = 15 \\ h {}^{2} = 12 \\ \boxed{h = 2 \sqrt{3} \text{ \: cm}}$