Question

find the perimeter of the window to the nearest tenth. perimeter: about \square cm

Explanation:

Step1: Identify the shape's perimeter components

The window is a semicircle with a diameter of 20 cm. The perimeter of a semicircular shape includes the curved part (half the circumference of the full circle) and the diameter. The formula for the circumference of a circle is \( C = \pi d \), so half the circumference is \( \frac{1}{2} \pi d \). Then we add the diameter (20 cm) to this curved length.

Step2: Calculate the curved length

Given \( d = 20 \) cm, the length of the semicircular arc is \( \frac{1}{2} \times \pi \times 20 = 10\pi \) cm. Using \( \pi \approx 3.1416 \), this is approximately \( 10 \times 3.1416 = 31.416 \) cm.

Step3: Add the diameter to the curved length

The total perimeter is the curved length plus the diameter: \( 31.416 + 20 = 51.416 \) cm. Rounding to the nearest tenth gives approximately 51.4 cm.

Answer:

51.4