A Norman window has the shape of a rectangle surmounted by a semicircle. If the perimeter of the whole window is 13.9 ft. give the area A of the window in square feet when the width is 3.3 ft. Use π

Answer 1

Let h be the height of the rectangle.

Width, w = 3.3

Let the radius of the semicircle, r = w/2

Perimeter, P = Circumference of half circle + w + 2h = 13.9

= πr + 2r + 2h = 13.9

h = (13.9 - πr - 2r)/2

Area, A = Area of Semicircle + Area of rectangle = πr²/2 + wh = πr²/2 + 2rh

A = π(3.3/2)²/2 + 2(3.3/2)(13.9-3.3π/2 - 3.3)/2

Can you complete the computation?

Answer 2

Draw and label a diagram.

The width of the window is the diameter of the semi-circle.

Determine area of the semi-circle.

Determine the circumference of the semi-circle

Subtract that from the entire perimeter.

Subtract the 3.3 width

The result is twice the length of the rectangle.

Now determine the area of the rectangle.

Add the two areas.