Answer:
Area: 2x² + 9x + 8
Perimeter: 6x + 18
Explanation:
To create an expression for the area, we will break the shape up into two shapes. Then, we will find the area of each of these shapes and lastly add them together. The formula for a rectangle's area is A = LW. I have attached a picture of how I broke this shape up below.
1st Area:
A = LW
A = (x)(x + 3)
A = x² + 3x
2nd Area:
A = LW
A = (x + 2)(x + 4)
A = x² + 6x + 8
Add them together by combining like terms:
x² + 3x + x² + 6x + 8
x² + x² + 3x + 6x + 8
2x² + 9x + 8
To create an expression for the perimeter, we will add all of the figure's sides together. Since some of the sides are not given, we will add the two congruent sides together to find these sides.
Adding together:
x + (x + 3) + 2 + (x + 4) + (x + 2) + ((x + 3) + (x + 4))
Combing like terms:
x + x + 3 + 2 + x + 4 + x + 2 + x + 3 + x + 4
x + x + x + x + x + x + 3 + 2 + 4 + 2 + 3 + 4
6x + 18