A dog is leashed to the corner of a house with a 20 ft long leash. How much running area does the dog have? Round your answer to the nearest square foot, if necessary. The dog has about ___ square feet of running area.

Given data

Length of leash = 20feet

The length is the same as the radius of  a virtual circle the dog is bound to make

But the Corner of the house will make an angle of 90 degrees

Therefore the house will form a sector out of the virtual circle the dog can run

round

Area = πr^2

Area = 3.142*20^2

Area = 1256.8 square feet

Area of Sector Formula

The area of a sector can be calculated using the following formulas,

Area of a Sector of Circle = (θ/360º) × πr^2

where, θ is the sector angle subtended by the arc at the centre, in degrees, and 'r' is the radius of the circle.

Area of a Sector of Circle = (90/360º) × 3.142*20^2

Area of a Sector of Circle = (1/4º) × 3.142*400

Area of a Sector of Circle =3.142*100

Area of a Sector of Circle = 314.2 square feet

Hence the area the Dog can run is given as

Dog Runnable area = Area of circle - Area of Sector Subtended by the corner of the house

= 1256.8 -  314.2

= 942.6 square feet

Learn more about circles here:

link

The dog's running area is approximately 942 feet².

Step-by-step explanation:

The dog is leashed to a fixed point, the leash has a length of 20 ft, therefore he can rotate around that point at the maximum distance equal to the length of the leash. This pattern forms a circle, but there is an obstruction, which is the corner of the house. This obstruction takes an arc of the original circle, so the running area of the dog is the area of the whole circle minus the area of the arc formed by the corner of the house.

The dog's running area is approximately 942 feet².

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step-by-step explanation: