The area of the room is 147.5 square feet so Michelle's reasoning was incorrect.
Step-by-step explanation:
Step 1:
To calculate the area of the given room, we divide the unknown shape into known shapes.
The room's shape is made of 2 rectangles.
The area of a rectangle is the product of its length and its width.
One rectangle has a length of 10 feet and a width of 12 1/2 feet.
The other rectangle has a length of 15 - 10 = 5 feet and a width of 4 1/2 feet.
Step 2:
The area of the first rectangle = (10)(12 1/2) = (10)(12.5) = 125 square feet.
The area of the second rectangle (10)(4 1/2) = (5)(4.5) = 22.5 square feet.
The total area of the room = 125 + 22.5 = 147.5 square feet.
Sum of exterior angle of a polygon is 360
90 + 10x + 5x + 45 = 360
135 + 15x = 360
15x = 360 - 135 = 225
x = 225/15 = 15
Largest exterior angles = 10x = 10(15) = 150 degrees.
So the angle A on the first diamond corresponds with angle Q, angle B with angle S, angle C with angle R, and angle D with angle P. So if angle D correspond (equals) angle P then x+34=97 and if angle R corresponds with C then 3y-13=83. From there just do some basic algebra to find the x and y values.
