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The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal size. A shade for the window will extend 4 inches beyond the perimeter of the window, show by the dashed line around the window. Each square in the window has an area of 100 square inches.
a. What is the area of the window? Use 3.14 for ππ.
b. What is the area of the shade? Round your answer to the nearest whole number.

 

 Mar 21, 2021
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First, we know that each square in the window has an area of 100 inch2. This means the dimensions are 10 x 10. 

 

To find the area of the window, I'm going to split up the square part and the semicircle. 

This means the area of the square part is (10 x 4) x (10 x 4) = 40 x 40 = 1600 inch2. This is because this area is 4 squares by 4 squares. 

Now, the area of the semicircle is \(\frac{1}{2} (10 \cdot 2)^2 π = 200π ≈ 628\)

This means the area of the window is 2228 inch2

 

The shade is 4 inches beyond, and so the dimensions of the 4 by 4 square would be (40 + 4 + 4) by (40 + 4 + 4). 

This means the area is 48 x 48 = 2304 

Then the semicircle's radius would be (20 + 4). Which means the area is \(\frac{1}{2} (20 + 4)^2π = 288π ≈ 904\)

This means the area of the shade is 3208 inch2

 Mar 22, 2021

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