Question

5. Given perimeter of 100 mm, determine each side of aregular decagon, find apothem, then find area.(round your answer to the nearest hundredth)E

Answer 1

Remember that

A regular decagon has 10 equal sides

so

perimeter P is equal to

P=10s

where

s is the length side

so

P=100 mm

100=10s

s=10 mm

answer Part 1)

each side is 10 mm

Part 2

Find apothem

the regular decagon can be divided into 10 isosceles triangle

see the attached image to better understand tje problem

applying trigonometric identity find the height of triangle (apothem)

we have that

tan(72)=h/5

h=5*tan(72)

h=76.94 mm

answer part 2

apothem is 76.94 mm

Part 3

Find the area

the area is equal to

A=(1/2)*(apothem)*s

A=(1/2)*76.94*10

A=384.71 mm2