A table with a round top is cut in half so that it can be used against a wall. After it is cut, the edge along the wall is 6 \text{ feet}6 feet6, space, f, e, e, t. What is the area AAA of the table after it is cut in half ?

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Answer 1 · 2018-04-19T23:24:29

#14.14# #"ft"^2#

The table cut in half is now the shape of a semicircle.

The area of a normal circle is #pir^2#, but since this is half of a circle, we will divide that by #2#:

#(pir^2)/2 = "area of a semicircle"#

#"r = radius"#

The length of the diameter is #6#, but we will divide that in half to find the radius, since that is what is needed in the equation:

#6/2 = 3#

Now substitute into the equation:

#(pir^2)/2 = "area of a semicircle"#

#(pi(3)^2)/2#

#(pi9)/2 rarr 4.5pi = 14.14#

So the area of the tabletop is #14.14# #"ft"^2#