Question

A rectangular building is 4 meters by 6 meters. A dog is tied to a rope that is 10 meters long, and the other end is tied to the midpoint of one of the long sides of the building. Find the total area of the region that the dog can reach (not including the inside of the building), in square meters.

Known Wrong Answers: 128.66
8.5pi
2pi
112.5pi
41pi

Answer 1

Answer:

50π−24square meters

Step-by-step explanation:

The area of the semicircle is given by the formula:

Area of semicircle= πr ^2/2

where r is the radius. In this case, r= 10 meters.Substituting the values into the formula:

Area of semicircle= 2π×(10) /2 = 100pi /2 = 50 square meters

Now, we need to subtract the area of the rectangle from the total area of the semicircle, as the dog cannot go inside the building. The area of the rectangle is given by:

Area of rectangle=length×width=4×6=24square meters

Therefore, the total area that the dog can reach (not including the inside of the building) is: 50π−24square meters

This is the answer in terms of (pi)

π and can also be approximated if needed!!! <33