Question 1131625

1.  The apothem can be found using the Pythagorean theorem->The statement is {{{True}}}
we know that

If ABC is an equilateral triangle (see the attached figure with letters to better understand the problem)

then 

{{{AB=BC=AC}}}

 {{{b=8.7/2 =4.35}}} cm 

Applying the Pythagorean Theorem

 {{{5^2 =a^2 +b^2 }}}
 {{{a^2=5^2 -b^2}}}
 {{{a^2=25 -4.35^2}}}
 {{{a^2 =sqrt(6.0775) }}} 
{{{a=2.47}}} cm 
{{{a=2.5}}} cm 



2.The apothem can be found using the tangent ratio->The statement is {{{True}}}

we know that

 {{{tan(30)=a/b}}}
 {{{a=b*tan(30)}}}
 {{{a=4.35*sqrt(3)/3  }}}
{{{a=2.5}}} cm 



3. The perimeter of the equilateral triangle is {{{15cm}}} ->The statement is {{{False}}}

we know that perimeter of the equilateral triangle is equal to

 {{{P=8.7*3=26.1cm}}}  



4. The length of the apothem is approximately {{{2.5}}} cm ->The statement is {{{True}}}

see 1. and 2.



5. The area of the equilateral triangle is approximately {{{65cm^2}}}->The statement is {{{False}}}

Applying the law of sines

 {{{A=(1/2) *8.7*8.7*sin( 60) }}}
{{{A=32.77 cm^2}}}  



therefore

the answer is:

The apothem can be found using the Pythagorean theorem

The apothem can be found using the tangent ratio

The length of the apothem is approximately {{{2.5cm}}}