The area of a semi-circle of radius 7 c.m. is

Semi-Circle Area Calculation

Understanding how to calculate the area of a semi-circle is a fundamental concept in geometry. A semi-circle is exactly half of a full circle. To find its area, we first need to know the formula for the area of a full circle and then divide it by two.

Radius Definition and Given Information

The radius of a circle (or semi-circle) is the distance from its center to any point on its circumference. In this particular problem, the radius of the semi-circle is given as 7 c.m.

Formula for Semi-Circle Area

The standard formula used to calculate the area of a full circle is:

$$\text{Area of Circle}=\pi r^2$$

Where:

- $\pi$ (pi) is a mathematical constant, commonly approximated as $\frac{22}{7}$ or $3.14159$.
- $r$ is the radius of the circle.

Since a semi-circle is precisely half of a circle, its area formula is derived by dividing the full circle's area by two:

$$\text{Area of Semi-Circle}=\frac{1}{2}\pi r^2$$

Step-by-Step Area Calculation

Let's apply the formula for the area of a semi-circle using the given radius:

- Given: Radius ($r$) = 7 c.m.
- Step 1: Write down the formula for the area of a semi-circle: $$\text{Area}=\frac{1}{2}\pi r^2$$
- **Step 2: Substitute the value of the radius $r=7$ c.m. and use the common approximation $\pi =\frac{22}{7}$:** $$\text{Area}=\frac{1}{2}\times \frac{22}{7}\times (7{)}^2$$
- **Step 3: Calculate the square of the radius, $(7{)}^2$:** $$(7{)}^2=7\times 7=49$$
- Step 4: Substitute this calculated value back into the formula: $$\text{Area}=\frac{1}{2}\times \frac{22}{7}\times 49$$
- **Step 5: Simplify the expression. Notice that the $7$ in the denominator of $\pi$ and one of the $7$ s from $49$ (since $49=7\times 7$) can be cancelled out:** $$\text{Area}=\frac{1}{2}\times 22\times \frac{49}{7}$$ $$\text{Area}=\frac{1}{2}\times 22\times 7$$
- Step 6: Perform the remaining multiplication: $$\text{Area}=(\frac{1}{2}\times 22)\times 7$$ $$\text{Area}=11\times 7$$ $$\text{Area}=77$$
- Step 7: Add the correct unit. Since the radius was given in c.m., the area will be in square centimeters: $$\text{Area}=77{\text{ cm}}^2$$

Final Area Result

The calculated area of the semi-circle with a radius of 7 c.m. is **77 cm${}^2$ **.