seamus is building a circular garden in his backyard. the rectangular back yard mesures 5y by 12y. the garden has a radius of 3y. what is the area of the remainig yard
(5y * 12y) - [π (3y)^2]
To find the area of the remaining yard, we first need to find the area of the circular garden and then subtract it from the area of the entire rectangular backyard.
The area of a circle can be found using the formula A = πr^2, where A is the area and r is the radius.
Given that the radius of the circular garden is 3y, we can substitute this value into the formula to find the area of the garden:
A_garden = π * (3y)^2
= π * 9y^2
= 9πy^2
Now, let's find the area of the entire rectangular backyard using its length and width:
A_backyard = length * width
= 5y * 12y
= 60y^2
Finally, we can find the area of the remaining yard by subtracting the area of the garden from the area of the entire backyard:
A_remaining_yard = A_backyard - A_garden
= 60y^2 - 9πy^2
= y^2(60 - 9π)
So, the area of the remaining yard is y^2(60 - 9π).