Question

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 289 in2. Round your answers to the nearest whole number.

Answer 1

Part 1

The area of the window is 6,439 in².

Part 2

The area of the shade is 7,739 in²

Explanation:

Part 1 out of 2

What is the area of the window? Use 3.14 for π .

Separate the palladium window into simpler shapes: a large square and a large semicircle. The large square is made up of 16 smaller squares and the large semicircle is made up of 5 smaller shapes. Each small square in the window has an area of 289 in2.

Find the area of the large square in the window.

289 × 16 = 4,624

The area of the large square in the window is 4,624 in2.

Find the side length of the large square in the window.

A = s2

4,624 = s

68 × 68 = s

68 = s

The side length of the large square in the window is 68 in.

Find the area of the semicircle in the window. The side length of the large square is equal to the diameter of the semicircle. Round your answer to the nearest whole number.

A = 1 /2 π r2

A = 1 /2

(3.14) (34)2

A = 1,815

The area of the semicircle in the window is 1,815 in2.

Add the areas to find the total area of the window.

A = 1,815 + 4,624

A = 6,439

The area of the window is 6,439 in².

Part 2 out of 2

What is the area of the shade? Round your answer to the nearest whole number.

Separate the shade into simpler figures: a large rectangle and a large semicircle.

Find the length of the rectangle in the shade by adding 4 inches to both sides of the length of the large square in the window.

s = 68 + 8

s = 76

The length of the rectangle is 76 in.

Find the width of the rectangle in the shade by adding 4 inches to the side length of the large square in the window.

s = 68 + 4

s = 72

The width of the rectangle is 72 in.

Find the area of the rectangle in the shade.

A = LW

A = 76 × 72

A = 5,472

The area of the rectangle in the shade is 5,472 in².

Find the area of the semicircle in the shade. The length of the large square in the shade is equal to the diameter of the semicircle in the shade. Round your answer to the nearest whole number.

A = 1 /2 π r2

A = 1 /2

(3.14) (38)2

A = 2,267

The area of the semicircle in the shade is 2,267 in².

Add the areas to find the total area of the shade.

A = 5,472 + 2,267

A = 7,739

The area of the shade is 7,739 in².