Answer:
The area and perimeter of a semi-circle with a radius of 5 cm is approximately 39.27 cm² and 35.71 cm respectively.
Step-by-step explanation:
The area and perimeter of a semi-circle can be calculated using certain formulas for a full circle and then dividing by 2 for the semi-circle.
Area of semi-circle:
The area of a full circle = πr². So, the area of a semi-circle is half of this. If the radius (r) is 5 cm, the area (A) would be:
⇒ A = (1/2)πr²
⇒ A = (1/2)π(5²)
∴ A = 25π/2 cm² or ≈ 39.27 cm² (rounded to the nearest hundredth)
Perimeter of semi-circle:
The perimeter of a full circle (also known as the circumference) is 2πr. But the perimeter of a semi-circle is half of this plus the diameter, so the perimeter is half the circumference plus the diameter or πr + 2r. For a semi-circle with a radius of 5 cm, the perimeter (P) would be:
⇒ P = πr + 2r
⇒ P = π(5) + 2(5)
∴ P ≈ 35.71 cm (rounded to the nearest hundredth)