Find the perimeter of a region bounded on three sides by a rectangle with a base of 600 ft and a height of 800 ft and bounded above by a semicircle with a radius of 300 ft. Use the approximation π = 3.14. (Do not include the lower half of the semicircle in the perimeter)
surely you know that the circumference of the semi-circle is 300π
so, add that to the 3 straight sides,
To find the perimeter of the region, we need to calculate the sum of the lengths of all the sides.
First, let's consider the rectangle. A rectangle has four sides, and in this case, two of the sides have lengths of 600 ft (the base) and the other two sides have lengths of 800 ft (the height). So the perimeter of the rectangle is:
Perimeter of rectangle = 2 * base + 2 * height
= 2 * 600 ft + 2 * 800 ft
= 1200 ft + 1600 ft
= 2800 ft
Next, let's calculate the length of the curved side of the semicircle. The circumference of a full circle is given by the formula:
Circumference of a circle = 2 * π * radius
Since we only want the semicircle, we divide the circumference by 2:
Length of curved side of semicircle = π * radius
= 3.14 * 300 ft
= 942 ft
Finally, we can find the perimeter of the entire region by adding the perimeter of the rectangle and the length of the curved side of the semicircle:
Perimeter of the region = Perimeter of rectangle + Length of curved side of semicircle
= 2800 ft + 942 ft
= 3742 ft
Therefore, the perimeter of the region is approximately 3742 ft.