Question

Struggling lol. Any help would be appreciated!

Answer 1

Answer:

Heptagon = 84 ft²

Octagon  = 186 yd²

Triangle = 48√3 m²

Step-by-step explanation:

$\textsf{area of a regular polygon}=\dfrac12ap$

where:

• $a$ = length of apothem
• $p$ = perimeter

Heptagon

a = 5.0 ft

p = 33.6 ft

⇒ area = 1/2 x 5.0 x 33.6 = 84 ft²

Octagon

a = 7.5 yd

p = 8 x 6.2 = 49.6 yd

⇒ area = 1/2 x 7.5 x 49.6 = 186 yd²

Triangle

Formula for the apothem of an equilateral triangle :

$a=\dfrac{s}{2\sqrt{3}}$  where $s$ = side length

a = 4, so:

$4=\dfrac{s}{2\sqrt{3}}$

$\implies 8\sqrt{3}=s$

Now we know the side length, we can calculate the perimeter (p):

p = 3 x 8√3 = 24√3

⇒ area = 1/2 x 4 x 24√3 = 48√3 m²