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)

click or tap here to enter text.

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

a)

b)

Step-by-step explanation:

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

Then the area of the rectangular room is:

The area of a semicircle is

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

Finally, the total area is:

b) The perimeter of a rectangle is:

The perimeter of a semi-circle is:

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:

Intersecting secant-tangent theorem states that if a tangent segment and a secant segment are drawn to a circle from an exterior point, then the square of the measure of the tangent segment is equal to the product of the measures of the secant segment and its external secant segment.so to break it down: 1. pq acts as the tangent and ps as the secant with an intersection at p.sr = 21rp = 3x + 3pq = 4x + 4following to equation: tangent squared = the two segments multiplied by each otherso (4x + 4) ^ 2 = (3x + 3) • (21) simplifies to 16x^2 - 31x - 47 = 0 or (16x - 47)(x + 1) x = -1 or x = 47/162. pq acts as the tangent and ps as the secant with an intersection at p (again! )sr = 16rp = xpq = 15(15) ^ 2 = 16 • x225 = 16xx = 225/163. the interesting chords are proportional to each other so a ratio is possible to set up: ap dp 10 3 + x = = —— = pc pb 8 xcross multiple to get 10x = (3 + x)(8)x = 12