Question

a stained glass window is shaped like a semicircle. the bottom edge of the window is 36inches long. what is the area of the stained glass window? round your answer to the nearest hundreth

Answer 1

The area of the semicircle with a diameter of 36 inches is calculated using the formula ½πr². The area is found to be 508.94 inches², which can also be expressed as 3.53 feet² after conversion.

Step-by-step explanation:

The question involves finding the area of a semicircle with a given diameter. Since the diameter is 36 inches, the radius r of the window is half of that, which is 18 inches (or 1.5 feet).

To calculate the area of a semicircle, we use the formula Area = ½πr², where π is approximately 3.14159 and r is the radius. Plugging in the radius of 18 inches, we get:

Area = 0.5 × π × (18 inches)²

Area = 0.5 × 3.14159 × 324

Area = 508.938 inches². When rounded to the nearest hundredth, this is 508.94 inches².

If we wanted to express this in square feet, since there are 144 square inches in a square foot, we would divide by 144 to convert inches² to feet².

Area in square feet = ≈508.94 inches² ÷ 144

Area in square feet = 3.5346 feet², which rounds to 3.53 feet².

Answer 2

The formula for the area of a semicircle is equivalent to the area if it were a circle divided by 2. Since the bottom edge of the window is 36 inches long, this means that its diameter is also 36 inches long. This gives an area of 508.94 square inches.

The solution is:

A = Acircle/2 = pi*r^2/2 = pi*(18)^2/2 = 508.94 in^2