A cow is tied to the long side of a barn 10 feet from the corner.The rope being used to tie the cow to the barn is 21 feet long .The barn measures 11 feet wide and 28 feet long, what is the total area of the space in which the cow can graze
I see a semicircle of radius 28ft, and a quarter circle of radius18ft, and another quarter circle of 7 ft. Compute the areas of those.
Opps, the other way, I see adding quarter circles on that end also, you have to add them in.
i need the answer too
To find the total area in which the cow can graze, we need to determine the shape of the grazing area and then calculate its area.
First, let's determine the shape of the grazing area. The cow is tied to a point on the barn 10 feet from the corner. The rope used to tie the cow is 21 feet long. This creates a circular grazing area with the barn corner as its center and the rope as its radius.
Next, let's find the radius of the circular grazing area. Using the Pythagorean Theorem, we can calculate the length of the hypotenuse of the right triangle formed by the barn's length, width, and the rope.
The hypotenuse of the right triangle is the rope, which is 21 feet long. The width of the barn is 11 feet, and the distance from the corner to the point where the cow is tied is 10 feet.
Using the Pythagorean Theorem: c^2 = a^2 + b^2, where c represents the hypotenuse and a, b represent the other two sides of the triangle.
c^2 = 10^2 + 11^2
c^2 = 100 + 121
c^2 = 221
Taking the square root of both sides, we find that c ≈ 14.87. Therefore, the radius of the circular grazing area is approximately 14.87 feet.
Now that we have the radius, we can calculate the area of the circular grazing area using the formula for the area of a circle: A = πr^2, where A is the area and r is the radius.
A = π * (14.87)^2
A ≈ 696.57 square feet
Thus, the total area in which the cow can graze is approximately 696.57 square feet.