Final answer:
The area of a semi-circle with a diameter of 28 cm can be found by first calculating the radius to be 14 cm, then using the formula for the area of a circle (πr²) and dividing by two since a semi-circle is half of a circle. The result should be presented with two significant figures due to the given radius having two significant figures.
Step-by-step explanation:
To find the area of a semi-circle with a given diameter, we first need to calculate the radius of the full circle. The radius is half of the diameter, so for a circle with a diameter of 28 cm, the radius (r) would be 14 cm. The area (A) of a full circle is determined by the formula A = πr². Hence, the area of the full circle with a radius of 14 cm would be A = π(14 cm)². To find the area of just the semi-circle, we simply take half of the area of the full circle because a semi-circle is half of a full circle. So, using this process, the area of the semi-circle would be A = π(14 cm)² / 2. When using a calculator, you might get a precise number with many digits, but we should limit our answer to two significant figures since the radius was provided with two significant figures. Therefore, the area of the semi-circle is approximately 4.5 m² after considering significant figures and converting from cm² to m².