# Bounded Regions

## Rectangle

The area equation for a rectangle is A=l*w. The area of the rectangle is 24 units squared. The slope-intercept form for the bottom line is y=-2 and point-slope form is y+2=0(x-0). The slope-intercept form for the top line is y=4 and the point-slope form is y-4=0(x-0). The slope-intercept form for the right line is x=1 and the point-slope form is y-1=3/0(x-1). The slope-intercept form for the left line is x=-3 and point-slope form is y-2=3/0(x+3). The domain of the shape is [-3,1] and -3<=x<=1. The range of the shape is [-2,4] or -2<=y<=4.

## Trapezoid

The area equation of a trapezoid is 1/2(b1+b2)h. The area of the trapezoid 16.5 units squared. The slope-intercept form for the bottom line is y=-1 and the point-slope form is y+1=0(x-0). The slope-intercept form for the top line is y=1/3x+5 and point-slope form is

y-5=1/3(x-0). The slope-intercept form for the left line is x=1 and point-slope form is y-1=5/0(x-1). The slope-intercept form for right line is x=4 and the point-slope form is y-2=5/0(x-4). The domain for this shape is [1,4] or 1<=x<=4. The range for this shape is [-1,5] or -1<=y<=5.

## Pentagon

To figure out the area for the pentagon I split it into two shapes a rectangle and a triangle then when I got the area for both I added them together. The area of a rectangle is A=l*w and the area of a triangle is A=1/2bh. The area of the pentagon is 30 units squared. The slope-intercept form for the bottom line is y=0 and point-slope form is y+2=0(x-0). The slope-intercept form for the top line is y=4 and the point-slope form is y-4=0(x-0). The slope-intercept is x=-4 and point-slope form is y+3=4/0(x+2). The slope-intercept form for the right/top is y=1x-2 and the point-slope form is y+2=1(X-0). The slope-intercept form for right/bottom is y=1x+6 and the point-slope form is y-6=1(x-0). The range for this shape is [0,4] or 0<=y<=4. The domain for this shape is [-4,4] or -4<=x<=4.

## Critical Writing

All of the shapes I worked was easy but the easiest was the first one which was the rectangle because it had all straight lines, it was a shape that i was familiar with more, it was just plain and simple. While the other shapes would have diagonal lines and straight lines which wasn't simple like the first one. All three figures would have a line that has the slope of zero or undefined. The easiest thing to solve for all three of them was the area the more harder things to find the slope-intercept form and the point-slope form. Finding the area was more harder on the pentagon because I had to split the shape into two which was a rectangle and triangle. When I got the area for the rectangle and the triangle I just added them together. It was easier to figure out the point-slope and slope-intercept form for the pentagon and the trapezoid because it atleast had a diagonal line not like the rectangle. To get the domain and range was really easy for the rectangle and the trapezoid but the pentagon I wasn't sure if the domain goes all the way to the point or it just stops when the bottom line ends.