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Tanzania [10]
3 years ago
10

The design for the palladium window shown includes a semicircular shape at the top. The bottom is formed by squares of equal siz

e. 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 169 in2. Round your answers to the nearest whole number.
Mathematics
1 answer:
9966 [12]2 years ago
7 0

Answer:

(a)\ Area = 3765.32

(b)\ Area = 4773

Step-by-step explanation:

Given

A_1 = 169in^2 --- area of each square

Shade = 4in

See attachment for window

Solving (a): Area of the window

First, we calculate the dimension of each square

Let the length be L;

So:

L^2 = A_1

L^2 = 169

L = \sqrt{169

L=13

The length of two squares make up the radius of the semicircle.

So:

r = 2 * L

r = 2*13

r = 26

The window is made up of a larger square and a semi-circle

Next, calculate the area of the larger square.

16 small squares made up the larger square.

So, the area is:

A_2 = 16 * 169

A_2 = 2704

The area of the semicircle is:

A_3 = \frac{\pi r^2}{2}

A_3 = \frac{3.14 * 26^2}{2}

A_3 = 1061.32

So, the area of the window is:

Area = A_2 + A_3

Area = 2704 + 1061.32

Area = 3765.32

Solving (b): Area of the shade

The shade extends 4 inches beyond the window.

This means that;

The bottom length is now; Initial length + 8

And the height is: Initial height + 4

In (a), the length of each square is calculated as: 13in

4 squares make up the length and the height.

So, the new dimension is:

Length = 4 * 13 + 8

Length = 60

Height = 4*13 + 4

Height = 56

The area is:

A_1 = 60 * 56 = 3360

The radius of the semicircle becomes initial radius + 4

r = 26 + 4 = 30

The area is:

A_2 = \frac{3.14 * 30^2}{2} = 1413

The area of the shade is:

Area = A_1 + A_2

Area = 3360 + 1413

Area = 4773

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