harpazo
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Section R.3
Geometry Essentials
Michael Sullivan
Textbook: College Algebra Edition 9
A norman window has the shape of a rectangle surmounted by a semicircle. Find the area of the Norman window if the length of the rectangle part is 6 inches and the width is 4 inches. How much wood frame is needed to enclose the window?
Solution:
Let me see how far I can go with this problem. Maybe I can slowly work my way to the answer.
Area of rectangle part of window is 6 inches x 4 inches or 24 (inches)^2.
Area of semicircle part of window is 1/2 (π r^2).
A = 1/2 • π (2 inches)^2
A = 1/2(4π) inches
A = 2π (inches)^2
Area of Norman window is
24 (inches)^2 + 2π (inches)^2.
Is this correct?
How much wood frame is needed to enclose the window?
Let P = perimeter of rectangle part of window.
P = 2l + 2w
P = 2(6 inches) + 2(4 inches)
P = 12 inches + 8 inches
P = 20 inches
Perimeter of Semicircle =
1/2 (π d).
Let PS = Perimeter of Semicircle.
PS = (1/2)(π)(4 inches)
PS = 2π inches.
The wood frame needed to enclose the Norman window is P + PS.
Answer to the wood frame part of the question is 20 inches + 2π inches.
Right? Wrong? Is there an easier method for solving this problem?
Geometry Essentials
Michael Sullivan
Textbook: College Algebra Edition 9
A norman window has the shape of a rectangle surmounted by a semicircle. Find the area of the Norman window if the length of the rectangle part is 6 inches and the width is 4 inches. How much wood frame is needed to enclose the window?
Solution:
Let me see how far I can go with this problem. Maybe I can slowly work my way to the answer.
Area of rectangle part of window is 6 inches x 4 inches or 24 (inches)^2.
Area of semicircle part of window is 1/2 (π r^2).
A = 1/2 • π (2 inches)^2
A = 1/2(4π) inches
A = 2π (inches)^2
Area of Norman window is
24 (inches)^2 + 2π (inches)^2.
Is this correct?
How much wood frame is needed to enclose the window?
Let P = perimeter of rectangle part of window.
P = 2l + 2w
P = 2(6 inches) + 2(4 inches)
P = 12 inches + 8 inches
P = 20 inches
Perimeter of Semicircle =
1/2 (π d).
Let PS = Perimeter of Semicircle.
PS = (1/2)(π)(4 inches)
PS = 2π inches.
The wood frame needed to enclose the Norman window is P + PS.
Answer to the wood frame part of the question is 20 inches + 2π inches.
Right? Wrong? Is there an easier method for solving this problem?