If the perimeter of regular pentagon ABCDE is 2015 inches, what is the area of triangle BCE

Question

Problem given by my teacher and i have no idea how to do it.

Answer 1

a regular polygon can have an inscribed circle and a circumscribed circle

a line segment drawn from the center of the regular pentagon perpendicular to any one of the sides is called an apothem

the apothem is also the radius of the inscribed circle

draw an apothem from the center of the regular pentagon perpendicular to side BC

if you extend this apothem up to point E you have doubled its length and this line segment will be the height of triangle BCE

line segment BC is the base of triangle BCE

the perimeter is 2015, so any one side has a measure of 2015/5=403 inches

the base BC=403 inches

the height is two times the apothem

to find the apothem use the following formula...

a=s/2tan(180/n) where s=403 (length of a side) and n=5 (# of sides)

a=403/2tan(36º) (180/5=36)

a=403/2(0.72654)

a=403/1.45308)

a=277.3419 inches

double the apothem to get the height

2a=2(277.3419)=554.6838

A=(1/2)(base)(height) for the area of the triangle

A=(1/2)(403)(554.6834)

A=(201.5)(554.6834)

A=111,768.79 square inches is the area

notice that we could have just multiplied the apothem by the base to get the area of the triangle because we multiplied the apothem by 2 and then took 1/2 of the base times the height

277.3419*403=111,768.79

you said you didn't know how to solve the problem so I solved it using what you know, the formula for the area of a triangle A=(1/2)bh and now you know how to find the apothem of a regular polygon