15 POINTS WILL MARK BRAINLIEST Find the area of the following shape. You must show all work to receive credit.

shape with vertices located at negative 4 comma 0, 0 comma 4, 2 comma 2, 0 comma 2, and 0, 0

36a

Step-by-step explanation:

First label all the lines:

Line 1- (0,0) and (0,2)

Line 2- (0,2) and (2,2)

Line 3- (2,2) and (0,4)

Line 4- (0,4) and (-4,0)

Line 5- (-4,0) and (0,0)

Next split the shape into two 

Now you have two triangles

Find the area of the first triangle

First triangle is Line 5, 4, and 1+ a little more

First find the distance of 5

Square root of (0-0) squared + (0+4) squared

Simplify:

0+16→ 16 squared is 4

Line 5 is 4

Now we find the distance of line 4:

Square root of (-4-0) squared +(0-4) squared

Simplify

16+16 → 32 squared is about 5.6

Line 4 is 5.6

Now lets find Line 1 but change it to (0,0) and (0,4)

Square root of (0-0) squared + (4-0) squared

Simplify

0+16→16 squared is 4

Let's label them, so Line 1 is the height and Line 5 is the base

The triangle area formula is 1/2bh

Let's plug everything in:

(1/2)4 times 4

Simplify 1/2 times 16 = 8

The area of triangle 1 is 8

 Now triangle two consists of lines 2, 3, and another one that has not been labeled. 

Not labeled line: (0,2) and (0,4)

Find Line 2:

Square root of (2-0) squared + (2-2) squared

Simplify

4+0 →4 squared is 2 

Line 2 is 2

Now let's find line 3:

Square root of (0-2) squared + (4-2) squared

Simplify

4+4→ 8 squared is 2.8

Line 3 is 2.8

Not labeled line:

Square root of (0-0) squared + (4-2) squared 

Simplify

0+4-> 4 squared is 2

Now label the line as base and height

Not labeled line is height and the base is line 2

Put it into the equation:

(1/2) 2 times 2

(1/2)4

Are of second triangle is 2

Now add both of them together and the area of the shape is 10 units