Answer:
24.8 ft (1 dp)
Step-by-step explanation:
Arc length of semicircle = [tex]\pi r[/tex] (where r is the radius)
Given:
- diameter = 4 ft
- ⇒ radius = 4 ÷ 2 = 2ft
- [tex]\pi[/tex] = 3.14
⇒ Arc length = 2 × 3.14 = 6.28 ft
Use Pythagoras' Theorem [tex]a^2+b^2=c^2[/tex] to find the hypotenuse of the right triangle with legs 2 ft and 4 ft:
[tex]\implies 2^2+4^2=c^2[/tex]
[tex]\implies c^2=20[/tex]
[tex]\implies c=\sqrt{20}=2\sqrt{5}\:\sf ft[/tex]
Therefore:
perimeter = 6 + 6.28 + 6 + 2 + 2√5
= 24.75213596...
= 24.8 ft (1 dp)
