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Elementary Geometry for College St...
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Elementary Geometry for College St...
Jeff and Helen want to carpet their family room, except for the entrance way and the semicircle in front of the fireplace, both of which they want to tile.
a) How many square yards of carpeting are needed?
b) How many square feet are to be tiled?
(a)
To find:
The number of square yards of carpeting are needed approximately.
Theorem:
In a circle of radius length r, the area A of a sector whose arc has degree measure m is given by
Postulate:
The area A of a rectangle whose base has length b and whose altitude has length h is given by
Formula:
The area of the semi-circle
Calculation:
Given that Jeff and Helen want to carpet their family room, except for the entrance way and the semicircle in front of the fireplace, both of which they want to tile.
We need to find out the number of square yards of carpeting are needed.
The area of carpeting needed = the area of rectangle – the area of semi-circle – the area of entry way which is in the sector shape.
To find the area of rectangle:
Base (b) = 6ft + 3ft + 3ft + 6ft = 18ft
Height (h) = 15ft
So, the area of rectangle =
To find the area of semi-circle:
Radius (r) = 3ft.
(b)
To find:
The number of square feet are to be tiled.
Chapter 8 Solutions
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