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d=43cm 3.1.1 Work out the area and perimeter of the semi-circle above​

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[tex] \huge \boxed{\mathbb{QUESTION} \downarrow}[/tex]

  • d = 43cm. Work out the area and perimeter of the ssemi-circle.

[tex] \large \boxed{\mathfrak{Answer \: with \: Explanation} \downarrow}[/tex]

Given that,

  • diameter (d) = 43 cm
  • So, radius (r) = 43/2 = 21.5 cm (radius is equal to half of the diameter in a circle)

Now, let's solve & find the area & perimeter of the semi-circle.

(1) Radius (r) = 21.5 cm

Area of a semi-circle = πr²/2

[tex]\downarrow[/tex]

[tex] \tt \frac{ \pi \: r ^{2} }{2} \\\tt = \frac{3.14 \times (21.5) ^{2} }{2} \\ \tt = \frac{3.14 \times 46.25}{2} \\ \tt = \frac{1451.465}{2} \\ = \boxed{\boxed{\bf 725.73 \: cm ^{2} }}[/tex]

(2) Radius (r) = 21.5 cm

Perimeter of the semi-circle = r (π + 2)

[tex]\downarrow[/tex]

[tex]\tt \: r(\pi + 2) \\ = \tt \: 21.5(3.14 + 2) \\ \tt = 21.5(5.14) \\ \tt = 21.5 \times 5.14 \\ = \boxed{\boxed{\bf 110.51 \: cm}}[/tex]

  • NOTE :- Since the value of π is not given in the question, I have taken it as 3.14. The answers can vary a little bit (just a little, so you can round the answers). These are the approximate values.
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