what is the area of a regular pentagon, with an apothem 14 in long and a side length 20 in long?
a. 1400 in^2
b.700 in^2
c.175 in^2
d.140 in^2

Question

what is the area of a regular pentagon, with an apothem 14 in long and a side length 20 in long? 
a. 1400 in^2
b.700 in^2
c.175 in^2
d.140 in^2

teacherspet02 · Answer

@Will.H

will.h · Answer

Regular pentagon are$$A=1/4 \sqrt{5(5+2\sqrt{5)}a^2}$$
Therefore after plugging a= 20 
Are would equal 688.19

michele_laino · Answer

hint:
we can apply this formula:
$$area = \frac{{erimeter \times apothem}}{2}$$

michele_laino · Answer

oops..
$$area = \frac{{perimeter \times apothem}}{2}$$

teacherspet02 · Answer

i got tht when i did it to, but i dont know what to do next bc that isnt an answer they want....?

michele_laino · Answer

wherein:
$perimeter=20 \times 5=...$

teacherspet02 · Answer

So A?

will.h · Answer

@Michele_Laino i feel like am missing something, what is it?

teacherspet02 · Answer

ohh i forgot to divide... thank you!

will.h · Answer

Good job

michele_laino · Answer

please wait

michele_laino · Answer

I have made a typo:
$$area = \frac{{perimeter \times apothem}}{2} = \frac{{100 \times 14}}{2} = 700$$

teacherspet02 · Answer

700 is right?

michele_laino · Answer

that's right!

will.h · Answer

Nicely done Michele

michele_laino · Answer

thanks!! :) @Will.H