Calculating the perimeter of a semi circle is an essential geometry skill. This guide will show you step-by-step how to find the perimeter of a semi circle given its radius.
Step 1: Show the Perimeter Formula
The formula for the perimeter \(P\) of a semi circle is given by:
\[ P = \pi \cdot r + 2 \cdot r = \pi \cdot r + d \]
Where:
- \(r\) is the radius of the semi circle.
- \(d\) is the diameter of the semi circle, which is \(2r\).
Step 2: Explain the Formula
In this formula:
- \(\pi \cdot r\) represents the length of the curved part of the semi circle.
- \(2 \cdot r\) or \(d\) represents the straight-line distance across the semi circle (diameter).
The perimeter of a semi circle is the sum of the curved length and the diameter.
Step 3: Insert Numbers as an Example
Let's say we have a semi circle with:
- Radius \(r = 7\) units
Step 4: Calculate the Final Value
First, we need to find the length of the curved part:
\[ \text{Curved Length} = \pi \cdot r \]
Substitute the values into the formula:
\[ \text{Curved Length} = \pi \cdot 7 \]
For \(\pi \approx 3.14\):
\[ \text{Curved Length} \approx 3.14 \cdot 7 \]
\[ \text{Curved Length} \approx 21.98 \, \text{units} \]
Next, we need to find the diameter:
\[ \text{Diameter} = 2 \cdot r \]
Substitute the values into the formula:
\[ \text{Diameter} = 2 \cdot 7 \]
\[ \text{Diameter} = 14 \, \text{units} \]
Finally, we sum the curved length and the diameter to find the perimeter:
\[ P = 21.98 + 14 \]
\[ P = 35.98 \]
So, the perimeter of the semi circle is approximately 35.98 units.
Final Value
The perimeter of a semi circle with a radius of 7 units is approximately 35.98 units.
