Question

Calculati aria rombului ABCD cu masura unghiului A=45 grade si perimetrul egal cu 8√7 cm. urgenttt..Dau coroana

Answer 1

Se determina lungimea laturii rombului, apoi se foloseste formula:

$\mathcal{A} = \ell \cdot \ell \sin A$

$\mathcal{P} = 4\ell =8\sqrt7 \Longrightarrow l = 2\sqrt7$

$\mathcal{A} =2\sqrt7\cdot2\sqrt7 \sin 45^0 = 4\cdot7\cdot\dfrac{\sqrt2}{2} =14\sqrt2 \ cm ^2$

Answer 2

P=8√7=>L=8√7/2=4√7. Ducem diagonala BC. IN ΔABC ducem inaltimea CM, M∈AB. FIE ΔAMC-dreptunghic si isoscel.AM≡MC, AC=4√7. Aplicam th pitagora ⇒AM²+MC²=AC² ⇒MC²+MC²=28 ⇒2MC²=28 ⇒MC²=14 ⇒MC=√14. AriaABCD= B*H=AB*MC =2√7*√14=2√98=2*7√2 ¸=>Aria ABCD=14√2