Odpowiedź:
1) a) 8 × 7 + 4 × 12 = 56 + 48 = 100 cm
b) 20² + h² = 29²
h² = 841 - 400
h² = 441
h = [tex]\sqrt{441}[/tex] = 21 cm
6 × 20 + 3 × 21 = 120 + 63 = 183 cm
2) 8² + 15² = k²
k² = 64 + 225
k² = 289
k = [tex]\sqrt{289}[/tex] = 17 cm
Obwód Δ ABF: 8 + 17 + 17 = 42 cm
3) [tex]\frac{a^{2}\sqrt{3} }{4}[/tex] = 25[tex]\sqrt{3}[/tex]
a²[tex]\sqrt{3}[/tex] = 100 [tex]\sqrt{3}[/tex]
a² = 100
a = [tex]\sqrt{100}[/tex] = 10 cm
10h = 70
h = 7 cm
V = Pp × h = 25[tex]\sqrt{3}[/tex] × 7 = 175[tex]\sqrt{3}[/tex] cm³
4) a) Podstawa: Trójkąt, a = 4 cm, h = 10 cm
Pp = [tex]\frac{a^{2}\sqrt{3} }{4}[/tex] = [tex]\frac{16\sqrt{3} }{4}[/tex] = 4[tex]\sqrt{3}[/tex] cm²
V = 4[tex]\sqrt{3}[/tex] × 10 = 40[tex]\sqrt{3}[/tex] cm³
b) Podstawa: Sześciokąt, a = 8 cm, h = 15 cm
Pp = [tex]\frac{3a^{2} \sqrt{3} }{2}[/tex] = [tex]\frac{192\sqrt{3} }{2}[/tex] = 96[tex]\sqrt{3}[/tex]
V = 96[tex]\sqrt{3}[/tex] × 15 = 1440[tex]\sqrt{3}[/tex] cm³
1440[tex]\sqrt{3}[/tex] : 40[tex]\sqrt{3}[/tex] cm³ = 36
Odp: 36 razy
