Geometry check my answers please :)

Question

Would this be correct??

A regular octagon rests on one of the flat sides and has a total height of 10 ft. What is the measure of one of the octagon’s sides? (1 pt.)

 360/8 = 45

180 - 45 = 135

135/2 = 67.5

sa = 67.7

a * tan (67.5) = 5

a= 5 / ( tan ( 67.5 ) )

a = 2.07 ft

The side of the octagon is 2*2.07 ft = 4.14 ft

Round to tenth = 4.2 ft

Answer 1

here's a little trick to get the answer

the height is basically twice the apothem

the apothem is the height of the bottom triangle (as well as all the others)

the central angle is 360/8=45°

the apothem bisects this angle so you have two congruent right triangles with the top central congruent angles each being 22.5°

tan=opposite/adjacent

the opposite side is 1/2 of one of the sides of the octagon

tan=(1/2)*side/adjacent but the adjacent is 5 (half of 10, the height or apothem)

tan22.5°=(1/2)*side/5

tan22.5°=side/10

10tan22.5°=side

10*0.41421356=side

side=4.1421356

side=4.1 feet

you could also find the area of one triangle using A=a^2ntan(180/n) where a=apothem, n=# of sides

after finding the area use A=(1/2)bh where you are given the area and the height (the apothem which is 5)

Answer 2

You are correct up to the rounding. Unless your instructor has specific instruction on rounding that would lead to a value of 4.14 being rounded up to 4.2, normally you would round 4.14 down to 4.1.