Question

A glass window is in the shape of a semicircle with dimensions shown.

1.2 meters
What is the approximate perimeter of the window? (Use 3.14 as an approximation for PI.)

Answer 1

To calculate the perimeter of a semicircular window, we need to find the length of the curved part (the semicircle) and add it to the diameter of the semicircle.

1. **Finding the Diameter**:
Given that the height of the semicircle is 1.2 meters, this height is the radius when the semicircle is placed upright. The diameter (\(d\)) is thus:
\[
d = 2 \times r = 2 \times 1.2 = 2.4 \text{ meters}
\]

2. **Finding the Curved Length (Half the Circumference)**:
The formula for the circumference of a full circle is \(C = 2\pi r\). Since we need the length of the semicircle, we take half of that:
\[
\text{Curved Length} = \frac{1}{2} \times 2\pi r = \pi r
\]
Substituting the radius:
\[
\text{Curved Length} = \pi \times 1.2
\]
Using \( \pi \approx 3.14 \):
\[
\text{Curved Length} \approx 3.14 \times 1.2 = 3.768 \text{ meters}
\]

3. **Calculating the Total Perimeter**:
The total perimeter \(P\) of the semicircular window is:
\[
P = \text{Curved Length} + \text{Diameter} = 3.768 + 2.4
\]
\[
P \approx 3.768 + 2.4 = 6.168 \text{ meters}
\]

Thus, the approximate perimeter of the window is **6.17 meters** when rounded to two decimal places.