To find the and of the , let's do each step separately.
Calculating the Perimeter
To determine the perimeter of the polygon, we must find the sum of its side lengths. This polygon has three vertices, so it is a . Let's draw it in a .
Before we can find the sum of the side lengths we must find the length of each side. We can use the to do this. Let's start with GE.
GE = sqrt((x_2-x_1)^2 + (y_2-y_1)^2)
GE = sqrt(( 6-( -1))^2+( -2- 5)^2)
GE=sqrt((6+1)^2+(-2-5)^2)
GE=sqrt(7^2+(-7)^2)
GE=sqrt(49+49)
GE=sqrt(98)
GE=sqrt(49*2)
GE=sqrt(49)*sqrt(2)
GE=7sqrt(2)
We continue by calculating the length of the other two sides EF and FG.
| Side
|
Coordinates
|
sqrt((x_2-x_1)^2+(y_2-y_1)^2)
|
Length
|
| EF
|
( 6,-2)
( 6,5)
|
sqrt(( 6- 6)^2+( 5-( -2))^2)
|
7
|
| FG
|
( 6,5)
( -1,5)
|
sqrt(( -1- 6)^2+( 5- 5)^2)
|
7
|
Now, let's calculate the triangle's perimeter. We do so by adding the three sides.
P=GE+EF+FG
P= 7sqrt(2)+ 7+ 7
P= 23.899494...
P≈ 23.90
The triangle's perimeter is approximately 23.90 units.
Calculating the Area
Now, let's calculate the of the triangle. Note that, because EF is vertical and FG is horizontal, they are . Therefore, the given triangle is a .
To calculate the , we can use the following formula.
A=1/2bh
In this formula, b is the length of the base of the triangle and h is the height. Since we are given a right triangle, we can arbitrarily choose the base and the height to be either of the perpendicular sides. Let's use EF as the height and FG as the base. They are both 7 units long, so now we can calculate the area.
A=1/2bh
A=1/2( 7)( 7)
A=1/2*49
A=49/2
A=24.5
The triangle's area is 24.5square units.
