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Welcome to the article A stained glass window is shaped like a semicircle The bottom edge of the window is 36 inches long What is the area of the. On this page, you will learn the essential and logical steps to better understand the topic being discussed. We hope the information provided helps you gain valuable insights and is easy to follow. Let’s begin the discussion!

A stained glass window is shaped like a semicircle. The bottom edge of the window is 36 inches long. What is the area of the stained glass window? Round your answer to the nearest hundredth.

Answer :

The area of the stained glass window is approximately 509.79 square inches.

To find the area of the stained glass window, which is shaped like a semicircle, we need to calculate the area of a full circle and then take half of that value, since a semicircle is half of a circle.

The formula for the area of a circle is given by [tex]\( A = \pi r^2 \)[/tex], where r is the radius of the circle.

Given that the bottom edge of the window, which is the diameter of the semicircle, is 36 inches long, we can find the radius by dividing the diameter by 2.

Thus, the radius r is [tex]\( \frac{36}{2} = 18 \)[/tex] inches.

Now, we can calculate the area of the full circle using the radius:

[tex]\[ A_{\text{full circle}} = \pi r^2 = \pi (18)^2 \][/tex]

[tex]\[ A_{\text{full circle}} = \pi \times 324 \][/tex]

[tex]\[ A_{\text{full circle}} = 324\pi \][/tex]

Since we need the area of a semicircle, we take half of the full circle's area:

[tex]\[ A_{\text{semicircle}} = \frac{1}{2} \times A_{\text{full circle}} \][/tex]

[tex]\[ A_{\text{semicircle}} = \frac{1}{2} \times 324\pi \][/tex]

[tex]\[ A_{\text{semicircle}} = 162\pi \][/tex]

Using the value of [tex]\( \pi \approx 3.14159 \)[/tex], we get:

[tex]\[ A_{\text{semicircle}} \approx 162 \times 3.14159 \][/tex]

[tex]\[ A_{\text{semicircle}} \approx 509.7868 \][/tex]

Rounding to the nearest hundredth, the area of the stained glass window is approximately 509.79 square inches.

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Rewritten by : Brahmana