Odpowiedź :
Odpowiedź:
Szczegółowe wyjaśnienie:
Zad 1.
P = [tex]\frac{a^{2}\sqrt{3} }{4}[/tex] = [tex]\frac{6^{2}\sqrt{3} }{4}[/tex] = [tex]\frac{36\sqrt{3} }{4}[/tex] = 9[tex]\sqrt{3}[/tex] (cm²)
Zad 2.
h = 103 cm
h = [tex]\frac{a\sqrt{3} }{2}[/tex]
[tex]\frac{a\sqrt{3} }{2}[/tex] = 103/*2
a[tex]\sqrt{3}[/tex] = 206/:[tex]\sqrt{3[/tex]
a = [tex]\frac{206}{\sqrt{3} }[/tex] = [tex]\frac{206\sqrt{3} }{3}[/tex]
Obw = 3a = 3 *[tex]\frac{206\sqrt{3} }{3}[/tex] = 206[tex]\sqrt{3}[/tex] (cm)
P = [tex]\frac{(\frac{206\sqrt{3} }{3})^{2}\sqrt{3} }{4}[/tex] = [tex]\frac{ \frac{42436 * 3 * \sqrt{3} }{9} }{4}[/tex] = [tex]\frac{127308\sqrt{3} }{36}[/tex] (cm²)
Zad. 3
Ten czworokąt to kwadrat.
R = 6 cm
R = [tex]\frac{\sqrt{2} }{2}[/tex]a
[tex]\frac{\sqrt{2} }{2}[/tex]a = 6/*2
a[tex]\sqrt2}[/tex] = 12/:[tex]\sqrt{2}[/tex]
a = [tex]\frac{12}{\sqrt{2} }[/tex] = [tex]\frac{12\sqrt{2} }{2}[/tex] = 6[tex]\sqrt{2}[/tex] (cm)
P = [tex]a^{2}[/tex] = [tex](6\sqrt{2}) ^{2}[/tex] = 36 * 2 = 72 (cm²)
Zad. 4
R = 10 cm
a = R = 10 cm
Dłuższa przekątna = 2a = 2 * 10 cm = 20 cm
Krótsza przekątna = a[tex]\sqrt{3}[/tex] = 10[tex]\sqrt{3}[/tex] cm
Obw = 6a = 6 * 10 cm = 60 cm
P = [tex]\frac{6a^{2}\sqrt{3} }{4}[/tex] = [tex]\frac{6 * 10^{2}\sqrt{3} }{4}[/tex] = [tex]\frac{600\sqrt{3} }{4}[/tex] = 150[tex]\sqrt{3}[/tex] (cm²)
Zad. 5
R = 20 cm
a - bok trójkąta
b - bok kwadratu
c - bok sześciokąta foremnego
R = [tex]\frac{a\sqrt{3} }{3}[/tex]
[tex]\frac{a\sqrt{3} }{3}[/tex] = 20/*3
a[tex]\sqrt{3}[/tex] = 60/:[tex]\sqrt{3}[/tex]
a = [tex]\frac{60 }{\sqrt{3} }[/tex] = [tex]\frac{60\sqrt{3} }{3}[/tex] = 20[tex]\sqrt{3}[/tex] (cm)
[tex]P_{trojkata}[/tex] = [tex]\frac{(20\sqrt{3})^{2}\sqrt{3} }{4}[/tex] = [tex]\frac{400 * 3 * \sqrt{3} }{4}[/tex] = [tex]\frac{1200\sqrt{3} }{4}[/tex] = 300[tex]\sqrt{3}[/tex] (cm²)
R = [tex]\frac{\sqrt{2} }{2}[/tex]b
[tex]\frac{\sqrt{2} }{2}[/tex]b = 20/*2
b[tex]\sqrt{2}[/tex] = 40/:[tex]\sqrt{2}[/tex]
b = [tex]\frac{40}{\sqrt{2} }[/tex] = [tex]\frac{40\sqrt{2} }{2}[/tex] = 20[tex]\sqrt{2}[/tex] (cm)
[tex]P_{kwadratu}[/tex] = (20[tex]\sqrt{2}[/tex])² = 800 (cm²)
c = R = 20 cm
[tex]P_{szesciokata}[/tex] = [tex]\frac{6 * 20^{2}\sqrt{3} }{4}[/tex] = [tex]\frac{6* 400\sqrt{3} }{4}[/tex] = [tex]\frac{2400\sqrt{3} }{4}[/tex] = 600[tex]\sqrt{3}[/tex] (cm²)
