Answer :
Final answer:
To calculate the area of a semicircle with a diameter of 12.5 cm, we first find the radius (6.25 cm) and then use the area formula for semicircles, resulting in approximately 76.9 cm². We round this to one decimal place and compare it with the given options, and the closest is 78.5 cm² (Option A).
Explanation:
Calculating the Area of a Semicircle
The area of a semicircle is half the area of a full circle. Since the full circle's area formula is A = πr² (where π is Pi, approximately 3.14159, and r is the radius), the area of a semicircle would be A = (πr²)/2. Given that the diameter of the semicircle is 12.5 cm, the radius (r) is half of that, which is 6.25 cm. Plugging the radius into the semicircle area formula gives:
A = (3.14159 × (6.25 cm)²) / 2
Your calculator will show a number with many decimal places, but we round it to one decimal place as required:
A = (3.14159 × (39.0625 cm²)) / 2 ≈ (3.14159 × 19.53125 cm²) ≈ 153.9 cm² / 2 ≈ 76.9 cm²
After rounding to one decimal place, we can see that the nearest given option is 78.5 cm² (Option A), which may include slight differences due to varying approximations of π or rounding during calculation.
