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, shown by the dashed line around the window. Each square in the window has an area of 100 i n 2. What is the area of the shade? Round your answer to the nearest whole number.

Question

Mathematics

Irene

6 October, 14:37

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, shown by the dashed line around the window. Each square in the window has an area of 100 i n 2. What is the area of the shade? Round your answer to the nearest whole number.

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Answers (1)

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Spunky · Answer 1

Area of the window:

A (window) = 16 · 100 + 1/2 · 20² π = 1600 + 200 π = 2,228

A (window + shade) = 48 · 40 + 1/2 · 24² π = 2,824.32

A (shade) = 2,824.32 - 2,228 = 596.32 ≈ 596 in²

Answer:

Area of the shade is 596 in².