Question

the stained glass window shown is a half - circle. what is the perimeter of the window? use 3.14 for π. show your work.

Explanation:

Step1: Find the circumference of the half - circle

The formula for the circumference of a full circle is $C = 2\pi r$ or $C=\pi d$. For a half - circle, the curved part length $l=\frac{1}{2}\pi d$. Let's assume the diameter $d$ of the half - circle is given (if not given, we need to measure or have it provided). Here we use the formula for the curved part of the half - circle.

Step2: Add the diameter to the curved part length

The perimeter $P$ of the half - circle window is the sum of the curved part length and the diameter. So $P=\frac{1}{2}\pi d + d$. If we factor out $d$, we get $P = d(\frac{\pi}{2}+ 1)$. Given $\pi = 3.14$, then $\frac{\pi}{2}+1=\frac{3.14}{2}+1=1.57 + 1=2.57$. So $P = 2.57d$.

Answer:

The perimeter of the half - circle window is $2.57d$, where $d$ is the diameter of the half - circle. If the diameter value is known, substitute it into the formula to get the numerical value of the perimeter.