SOLUTION: Find the perimeter and the area of the shaded region use 3.14 for pie. A retangle shaded with a half circle on one end. The width is 25 ft. the height is 20 ft. I have the answer

Algebra ->  Rectangles -> SOLUTION: Find the perimeter and the area of the shaded region use 3.14 for pie. A retangle shaded with a half circle on one end. The width is 25 ft. the height is 20 ft. I have the answer      Log On


   

Question 165223: Find the perimeter and the area of the shaded region use 3.14 for pie.
A retangle shaded with a half circle on one end. The width is 25 ft. the height is 20 ft. I have the answers but I need to know how to work the problem.
Answer: Perimeter = 101.4 ft
Area = 343 ft2
Can someone please help by showing me how to work the problem?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
area of rectangle:
width*height
25*20 = 500 square feet
.
area of half circle:
area for a full circle = (pi)r^2
half circle would be half of the above:
(1/2)(pi)r^2
plugging in our values:
(1/2)(3.14)10^2
(1/2)(3.14)100
(3.14)50
157 square feet
.
Area of shaded region is:
"area of rectangle" - "area of half circle"
500 - 157 = 343 square feet
.
Perimeter:
Edge along the rectangle:
height + 2(width)
20 + 2(25)
20 + 50
70 feet
.
Edge along the half-circle:
"circumference of a full circle" is
(pi)(d)
we only want half of that so:
(1/2)(pi)(d)
(1/2)(3.14)(20)
(3.14)(10)
31.4 feet
.
Perimeter then is:
70 + 31.4 = 101.4 feet