Perimeter: P =(12+sqrt(2)) units Area: A=10square units
Practice makes perfect
Let's find the perimeter and the area of the figure one at a time.
Perimeter
To determine the perimeter of the polygon, we must find the sum of its side lengths. This polygon has four vertices, so it is a quadrilateral. Let's denote the vertexes of this polygon.
Before we can find the sum of the side lengths, we must find the length of each side. We can use the Distance Formula to do this. Let's start with AD.
The quadrilateral's perimeter is equal to 12+sqrt(2) units.
Area
Now, we can find the area of our quadrilateral. To do it, let's divide it into a triangle and a rectangle.
The area of our quadrilateral is the sum of areas of the triangle and the rectangle.
A_(ABCD) = A_(AED) + A_(EBCD)
Let's begin by calculating the area of a triangle. To do so, we will use the formula for area of a triangle.
A = 1/2bh
Here, AE is the base b of our triangle and ED is the height h. We can use the Distance Formula again to find these lengths.
Side
Coordinates
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
Length
AE
( -3,1) ( -1,1)
sqrt(( -1-( -3))^2+( 1- 1)^2)
2
ED
( -1,1) ( -1,-1)
sqrt(( -1-( -1))^2+( -1- 1)^2)
2
By substituting these lengths into our formula, we can calculate the area.
The area of the triangle is 2square units. Next, we will find the area of the rectangle.
We can do it by multiplying its base by its height.
A=bh
Here, CD is the base b and ED is the height h. We already know these lengths, so we can substitute them into the formula to find the area.
