In order to find the side lengths of the polygon use the Distance Formula and, to find the area, separate the polygon into small rectangles and a triangle.
Perimeter: 32+3sqrt(2) units Area: 49.5 units square
Practice makes perfect
We will draw a polygon ABCDEFG with the following vertices.
A(1,1), B(10,1), C(10,8), D(7,5),
E(4,5), F(4,8), G(1,8)
Let's plot these points on the coordinate plane and connect them to draw the polygon.
Now, we will find the lengths of the polygon by using the Distance Formula.XY=sqrt(( x_1- x_2)^2+( y_1- y_2)^2)
In the formula, XY is the distance between the points X and Y, ( x_1,y_1) is the coordinates of X, and ( x_2,y_2) is the coordinates of Y. Now, let's find the length of each side of the polygon ABCDEFG by applying the formula. We will substitute the points A(1,1) and B(10,1), to find the length AB to start.
Thus, the perimeter is 32+3sqrt(2) units. Next, we will find its area by separating it into small rectangles and a triangle as the following.
We will find the area of each rectangle A_R and the area of the triangle A_T by using the formulas.
A_R= b h and A_T= b h/2
In the formula, b is the base and h is the height.
Area
Base
Height
A=bh or A=bh/2
Result
A_1
b=3
h=7
A_1= 3* 7
21
A_2
b=3
h=4
A_2= 3* 4
12
A_3
b=3
h=4
A_3= 3* 4
12
A_4
b=3
h=3
A_4=3* 3/2
4.5
Finally, we can find the total area A by adding the smaller areas together.
