Question

8 placas identicas na forma de losango, cujo lado mede 15cm monta um mosaico. A area frontal desse mosaico mede: Valendo 30pts

Answer 1

Boa noite Cintia!

Solução!

Fazendo!

$4\times 90\°=360\º\\\\\\ \alpha= \dfrac{360\º}{8} \\\\\\\ \alpha=45\º$

Usando a relação trigonometrica!

$\dfrac{h}{15}= \dfrac{ \sqrt{2} }{2}\\\\\\ 2h=15 \sqrt{2}\\\\\\\\\ h= \dfrac{15 \sqrt{2} }{2} \\\\\\\\ D1=D2$

Area de um losango!

$A_{losango}= \dfrac{D1 \times D2}{2} \\\\\\ A_{losango}= \dfrac{15 \sqrt{2} \times15 \sqrt{2} }{2} \\\\\\ A_{losango}= \dfrac{(15 \times15 )\sqrt{2} }{2}\\\\\\\ A_{losango}= \dfrac{225 \sqrt{2} }{2}$

$Area_{Mosaico}= \dfrac{8 \times 225 \sqrt{2}}{2} \\\\\\ Area_{Mosaico}= 4\times 225 \sqrt{2} \\\\\\ Area_{Mosaico}= 900 \sqrt{2} cm ^{2}$

Boa noite!

Bons estudos!