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Question 1

Question 2

1) n = 3. r = a*√3/6 = 2√3; a = 2*6 = 12; R = a√3 = 12√3; P = 3a = 36;
S = a^2*√3/4 = 144√3/4 = 36√3
2) n = 4; R = a√2 = 14√2; a = 14; r = a/2 = 7; P = 4a = 56; S = a^2 = 196
3) n = 5; P = 5a = 45; a = 9;
$R=a\sqrt{ \frac{5+ \sqrt{5} }{10} }=9\sqrt{ \frac{5+ \sqrt{5} }{10} }$ ≈ 7,656
$r=a \sqrt{ \frac{5+2 \sqrt{5} }{20} } =9\sqrt{ \frac{5+2 \sqrt{5} }{20} }$ ≈ 6,194
$S= \frac{ \sqrt{5}* \sqrt{5+2 \sqrt{5} } }{4}*a^2= \frac{81}{4}*\sqrt{5}* \sqrt{5+2 \sqrt{5} }$ ≈ 139,36
4) n = 6; S = 3/2*a^2√3 = 48√3; a^2 = 48*2/3 = 32; a = √32 = 4√2
R = a = 4√2; r = a/2*√3 = 4√2/2*√3 = 2√6; P = 6a = 24√2

Как видите, с пятиугольником сложнее всего.

mefody66_zn · Answer 1 · 2018-05-10T00:01:29+0000

1) n = 3. r = a*√3/6 = 2√3; a = 2*6 = 12; R = a√3 = 12√3; P = 3a = 36;
S = a^2*√3/4 = 144√3/4 = 36√3
2) n = 4; R = a√2 = 14√2; a = 14; r = a/2 = 7; P = 4a = 56; S = a^2 = 196
3) n = 5; P = 5a = 45; a = 9;
$R=a\sqrt{ \frac{5+ \sqrt{5} }{10} }=9\sqrt{ \frac{5+ \sqrt{5} }{10} }$ ≈ 7,656
$r=a \sqrt{ \frac{5+2 \sqrt{5} }{20} } =9\sqrt{ \frac{5+2 \sqrt{5} }{20} }$ ≈ 6,194
$S= \frac{ \sqrt{5}* \sqrt{5+2 \sqrt{5} } }{4}*a^2= \frac{81}{4}*\sqrt{5}* \sqrt{5+2 \sqrt{5} }$ ≈ 139,36
4) n = 6; S = 3/2*a^2√3 = 48√3; a^2 = 48*2/3 = 32; a = √32 = 4√2
R = a = 4√2; r = a/2*√3 = 4√2/2*√3 = 2√6; P = 6a = 24√2

Как видите, с пятиугольником сложнее всего.