Question

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)?

Answer 1

`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.`