A circular pond will be placed on a square piece of land. The length of a side of the square is 2x. The radius of the pond is x. The part of the square not covered by the pond will be planted with flowers. What is the area of the region that will be planted with flowers? Write your answer in factored form.

Step-by-step explanation:

The land on which the pond would be placed is a square. The formula for determining the area of a square is expressed as

Area = L²

The length of a side of the square is 2x. This means that the area of the land would be

Area = (2x)² = 4x²

The pond is circular and the formula for determining the area of a circle is

Area = πr²

Where

π is a constant

The radius of the pond is x. Therefore, area covered by the pond is

Area = π × x² = πx²

The part of the square not covered by the pond will be planted with flowers. Therefore, the area of the region that will be planted with flowers is

4x² - πx²

= x²(4 - π)

there are lots of ways.   pick's theorem tells us if the vertices are lattice points the area a is

a = b/2 + i - 1

where b is the number of boundary lattice points and i is the number of interior lattice points.

in the figure i count b=16, i=50 so

a = 8 + 50 - 1 = 57

let's try the shoelace formula.   the area is half the sum of the cross products of the sides.  

a(-2,6)   -2(2)-6(-5) = 26

b(-5,2)   -5(-3) - 2(-2) = 19

c(-2,-3) -2(-3) - (-3)(4) = 18

d(4,-3)   4(3) - (-3)(5) = 27

e(5,3)   5(3) - 3(1) = 12

f(1,3)     1(6) - 3(-2) = 12

a(-2,6)

each of the cross products is twice the area of the triangle with the associated side and one vertex the origin. so the area of abo=26/2=13.

area = (1/2) (26 + 19 +   18 + 27 + 12 + 12) = 57

that checks!

the final price would be 29.6925

step-by-step explanation:

39.59 minus 25% equals 29.6925