A community group is building a playground on a rectangular lot of land. The lot measures 6x by 9x and they want to cut out an area for a circular jungle gym with a radius of 4x. How much of the land will be left over after the jungle gym is built? (1 point)

To find out how much land will be left over after the jungle gym is built, we need to calculate the area of the rectangular lot and subtract the area of the circular jungle gym.

Let's start by calculating the area of the rectangular lot:
Area of a rectangle = length * width
Given that the length is 6x and the width is 9x, we can calculate the area as follows:
Area of rectangle = 6x * 9x = 54x^2

Next, let's calculate the area of the circular jungle gym:
Area of a circle = π * radius^2
Given that the radius is 4x, we can calculate the area as follows:
Area of circle = π * (4x)^2 = 16πx^2

Now, we can subtract the area of the circular jungle gym from the area of the rectangular lot to find the amount of land left over:
Land left over = Area of rectangle - Area of circle
Land left over = 54x^2 - 16πx^2

Since we don't have the exact value for π, we'll leave the answer in terms of π and x squared:
Land left over = (54 - 16π)x^2

Therefore, the amount of land left over after the jungle gym is built is (54 - 16π)x^2.

area of lot = (6x)(9x) = 54x^2

area of circle = π(4x)^2 = 16πx^2

amount left over = 54x^2 - 16πx^2
= (54-16π)x^2