In this case, we'll have to carry out several steps to find the solution.
Step 01:
Data:
leg of the star:
side = 20 ft
height = 19 ft
regular pentagon:
Step 02:
geometry:
area:
area of the legs of the star (triangle):
A = (base * height) / 2
s² = h² + b²
(20 ft)² = (19 ft)² + b²
400 ft² - 361 ft² = b²
39 ft² = b²
[tex]b=\text{ }\sqrt{39ft²}=6.25\text{ ft}[/tex]
base = 2 * b = 2 * 6.25 ft = 12.50 ft
total area of the legs of the star:
[tex]total\text{ area = 5*}\frac{(12.50\text{ ft * 19ft\rparen}}{2}=593.75\text{ ft^^b2}[/tex]
area of the center pentagon:
A = 1/2 a 5 s
[tex]pentagon\text{ area = }\frac{1}{2}*(8.5\text{ ft\rparen *5*\lparen12.50ft\rparen = 265.63 ft^^b2 }[/tex]
The answer is:
total area of the legs of the star = 593.75 ft²
area of the center pentagon = 265.63 ft²
