Let's think about the perimeter and area one at a time.
Perimeter
To find the perimeter, we need the lengths of all sides of the figure. Two of these are parallel to the x-axis, so we can find their lengths by counting the number of squares between their endpoints.
The top and bottom sides are both 6 units long. We can find QT and RS using the Distance Formula. The coordinates of the points are Q(-4,3), T(-2,-3), R(2,3), and S(4,-3). First we will calculate QT.
The base and height of both triangles are 2 and 6 units, respectively. To find their total area, we can use the formula for area of a triangle twice.
2A=2(b h/2) ⇒ 2(2( 6)/2)=12 units^2
The can calculate the area of the rectangle using the fact that the length is 6 units and the width is 4 units.
A= l w ⇒ 6( 4) = 24units^2
The total area of the figure is the sum of the areas of the triangles and the rectangle.
12+24 = 36 units^2
