Understanding the Area of a Semi-Circle: Formulas and Calculations

The area of a semi-circle is a fundamental concept in geometry that often appears in various practical applications. A semi-circle is essentially half of a circle, and its area can be calculated using the area of the full circle and then dividing it by two. Let's break down the process and explore the relevant formulas.

Basic Formula for Circle Area

The area of a circle is given by the formula:

A _ circle π r 2

Where:

r represents the radius of the circle. π (pi) is a mathematical constant approximately equal to 3.1416.

To find the area of a semi-circle, we simply need to take half of the area of the circle:

A _ semi -circle 1 2 × π r 2

Example Calculation

Suppose the radius r is 1 unit:

Calculate the area of the circle: A _ circle π 1 2 π 3.1416 Divide the result by 2 to get the area of the semi-circle: A _ semi -circle 1 2 × π π 2

Therefore, the area of the semi-circle is π 2 square units.

Another Example with Given Dimensions

Let's consider a circle with a diameter of 42 cm. First, we calculate the radius:

radius diameter 2 42 2 21

Now, we use the area formula for a circle:

A _ circle 21 2 × π 441 × π

Dividing this by 2 to find the area of the semi-circle:

A _ semi -circle 441 2 × π 220.5 × π

The result, when rounded to two decimal places, is approximately 692.37 square centimeters.

Conclusion

Understanding the area of a semi-circle is crucial in many real-world applications, from designing buildings to creating art. Whether you are working with theoretical or practical dimensions, being able to calculate the area of a semi-circle using the steps outlined here will serve you well in both scenarios.