A large dining room table is in the shape of a semicircle with a diameter of 12 feet. What is the area of the table? (Use #pi# = 3.14)?

1 Answer
mimi
Jun 15, 2017

#A=18pi ft^2 = 56.549 ft^2#

Explanation:

Given:
shape #=# semicircle [half of a circle]
#d = 12 ft#
#Area = ?#

Formulas:
Area of Circle#= pir^2#
#d=2r# [Remember radius is half the length of the diameter!]
#pi=3.14#

Since a semicircle is HALF of a circle, multiply the area of the circle by #(1/2)# to get the area of a semicircle:
Area of Circle#= pir^2# #-># Area of Semicircle#=(1/2)pir^2#

The formula needs the RADIUS, not the DIAMETER. Divide diameter by #2# to get radius.
#d=2r#
#12=2r#
#r=6#

Substitute values for variables in the formula for *area of a semicircle.*
#A=(1/2)pir^2#
#A=(1/2)pi(6)^2#
#A=(1/2)pi(36)#
#A=18pi = 56.549#

The area of the dining room table is #18pi ft^2# or #56.549 ft^2.#

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