Let's determine the perimeter and area one at the time.
Perimeter
To find the perimeter, we have to determine the length of the three unknown sides in the shape. Two of these sides are the hypotenuse of a right triangle. Therefore, we can determine their lengths with the Pythagorean Theorem.
3^2+3^2=c^2 ⇔ c=3sqrt(2)
3^2+6^2=c^2 ⇔ c= 3sqrt(5)
Let's add this information to the diagram. We will also add a new segment to find the length of the remaining side.
The last side can also be determined with the Pythagorean Theorem.
3^2+6^2=c^2 ⇔ c=3sqrt(5)
When we know the last side, we can determine the shape's perimeter.
5+3sqrt(5)+3+2+3sqrt(5)+3sqrt(2)≈ 27.7 mi.
Area
To find the area we will divide the shape into two triangles and one rectangle.
To calculate the triangles' area we need their base and height, and to calculate the rectangle's area we need its width and length. From the diagram we see that we have these dimensions and we can find the shape's area by adding these.
1/2(3)(6)+(2)(9)+1/2(3)(9)=40.5 mi.^2
