# What is the area enclosed by the graph of

the absolute value of (3x)+ the absolute value of (3y)=12?

what area are you looking for??

ar eyou looking for the area of a cylinder or what??

## To find the area enclosed by the given equation in the x-y coordinate plane, we need to first understand the shape of the graph.

The equation |3x| + |3y| = 12 represents a geometric shape called a rhombus. A rhombus is a quadrilateral with four sides of equal lengths, but the angles are not necessarily equal.

To determine the dimensions and orientation of the rhombus, we can manipulate the equation by breaking it down into four cases based on the absolute value signs.

Case 1: When x and y are both positive, the equation becomes 3x + 3y = 12.

Case 2: When x is positive and y is negative, the equation becomes 3x - 3y = 12.

Case 3: When x is negative and y is positive, the equation becomes -3x + 3y = 12.

Case 4: When x and y are both negative, the equation becomes -3x - 3y = 12.

Now, we can find the intercepts for each case by setting one variable to zero at a time.

Case 1:

Setting x = 0, we get 3y = 12, which gives us y = 4.

Setting y = 0, we get 3x = 12, which gives us x = 4.

So, the points on the graph in this case are (0,4) and (4,0).

Case 2:

Setting x = 0, we get -3y = 12, which gives us y = -4.

Setting y = 0, we get 3x = 12, which gives us x = 4.

So, the points on the graph in this case are (0,-4) and (4,0).

Case 3:

Setting x = 0, we get 3y = 12, which gives us y = 4.

Setting y = 0, we get -3x = 12, which gives us x = -4.

So, the points on the graph in this case are (0,4) and (-4,0).

Case 4:

Setting x = 0, we get -3y = 12, which gives us y = -4.

Setting y = 0, we get -3x = 12, which gives us x = -4.

So, the points on the graph in this case are (0,-4) and (-4,0).

Plotting these four points on the x-y coordinate plane, we get a rhombus-shaped graph.

Finally, to find the area of the rhombus, we can use the formula:

Area = (diagonal1 * diagonal2) / 2

where in this case, the diagonals of the rhombus are the distances between the four points we found earlier.

I hope this explanation helps you understand how to find the area enclosed by the given equation!