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Which has a smaller perimeter with the same area of 36 square units, a regular pentagon, a regular hexagon, or a regular octagon? PLEASE EXPLAIN IN THE SIMPLEST WAY The answer is on the board

Which has a smaller perimeter with the same area of 36 square units, a regular pentagon, a regular hexagon, or a regular octagon? PLEASE EXPLAIN IN THE SIMPLEST WAY The answer is on the board

Elementary Geometry For College Students, 7e
Elementary Geometry For College Students, 7e
7th Edition
ISBN:9781337614085
Author:Alexander, Daniel C.; Koeberlein, Geralyn M.
Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.
ChapterP: Preliminary Concepts
SectionP.CT: Test
Problem 1CT
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Which has a smaller perimeter with the same area of 36 square units, a regular pentagon, a regular hexagon, or a regular octagon? PLEASE EXPLAIN IN THE SIMPLEST WAY The answer is on the board
(3) (2) Area: 36 59. units Compare the perimeters of Pentagon, hexagon, ochagen. Soln. Since the area is A = san (36)= (5an ) 2 72 = San 22= sa २ 72 n = S (17(n-3) tan 2 (22)/(1-_ ((--)) - 72 -Zan n (10 (20)) २५ 1244 - 5 tan (2(2x)) h ter/alans)) २५ 2 S = 1 144 (5 (1-₂) to 144 n tant (13 (1-2) 144 n ton (²) Pentym: n=5 S=1 144 28-8 tan (7) S=4.574322333 P = 5 (5) P = 22-87161167 dmits) Haag: n=6 S=1 144 6 ton (((-2)) 26) 24 : 3.722911436 P= 6(S) = 22.33451662 Octagon S=\ : n=8 144 S = 2.7905 39 163 P: 8 (5) P: 21.844 31331
Transcribed Image Text:(3) (2) Area: 36 59. units Compare the perimeters of Pentagon, hexagon, ochagen. Soln. Since the area is A = san (36)= (5an ) 2 72 = San 22= sa २ 72 n = S (17(n-3) tan 2 (22)/(1-_ ((--)) - 72 -Zan n (10 (20)) २५ 1244 - 5 tan (2(2x)) h ter/alans)) २५ 2 S = 1 144 (5 (1-₂) to 144 n tant (13 (1-2) 144 n ton (²) Pentym: n=5 S=1 144 28-8 tan (7) S=4.574322333 P = 5 (5) P = 22-87161167 dmits) Haag: n=6 S=1 144 6 ton (((-2)) 26) 24 : 3.722911436 P= 6(S) = 22.33451662 Octagon S=\ : n=8 144 S = 2.7905 39 163 P: 8 (5) P: 21.844 31331
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