Question

On a blueprint, a rectangular room 14 feet by 12 feet has a semicircular sitting area attached with a diameter of 12 feet.

(a) What is the total area of the room and the sitting area? Show your work. (2 points)

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(b) What is the perimeter of the room (including the sitting area)? Show your work. (2 points)

Answer 1

a)
`A=224.55\ ft^2`

b)
`P = 58.85\ ft`

Explanation:

a) The area of a rectangle is calculated as the product of its length by its width.

`A = lw`

Then the area of the rectangular room is:

`A = 14 * 12\\\\A = 168\ ft ^ 2`

The area of a semicircle is
`A = (1)/(2)\pi r ^ 2`

We know that the diameter is 12 feet, then the radius is:

`r = (12)/(2) = 6\\\\r = 6\ ft`

`A = (1)/(2)\pi(6) ^ 2\\\\A = 56. 55 ft ^ 2`

Finally, the total area is:

`A=56. 55\ ft ^ 2+168\ ft ^ 2`

`A=224.55\ ft^2`

b) The perimeter of a rectangle is:

`P = 2l + 2w`

The perimeter of a semi-circle is:

`P = 0.5 * 2\pi r`

In this case r = 6

Since the semi-circle is attached to one of the sides of the room and its diameter is 12 feet, you cannot add one of the sides of rectangle that measures 12 feet to the perimeter (Observe the figure attached, which is not drawn to scale).Then the perimeter is:

`P = (12 + 2 * 14)+(0.5 * 2\pi (6))\\\\P = 58.85\ ft`