Answer
perimeter=14.8
area=10
Work Step by Step
Find the length of each side.
Using the ruler postulate:
top=$|-3-3|=|-6|=6$
right=$|1-(-1)|=|2|=2$
bottom=$|-1-3|=|-4|=4$
Using the distance formula, given endpoints of (-3,1) and (-1,-1):
$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$
$d=\sqrt{(-1-(-3))^2+(-1-1)^2}$
$d=\sqrt{(2)^2+(2)^2}$
$d=\sqrt{4+4}$
$d=\sqrt{8}$
$d=2.8$
Sum the lengths of the sides to find the perimeter.
$P=6+2+4+2.8=14.8$
To find the area, separate the figure into a rectangle and a triangle. Use the formulas for area and substitute. Add the areas of the rectangle and triangle to find the area of the figure.
The rectangle has base(b)=4 and height(h)=2.
$A_1=bh=4\times2=8$
The triangle has base(b)=2 and height(h)=2.
$A_2=\frac{1}{2}bh=\frac{1}{2}(2)(2)=2$
$A=A_1+A_2=8+2=10$
