We want to find the area of the given trapezoid. We can think of the trapezoid as two triangles to find the area. Let's see the diagram!
Now we will find the area of each triangle. We can see that the height h of the top triangle is 7 miles and the height of the bottom triangle is 4 miles. The base b for both triangles is 10 miles.
Next, we substitute these values into the formula for the area of a triangle.
A=1/2bh
Substitute
Evaluate
Triangle 1
A_1=1/2( 10)( 7)
A_1=35mi^2
Triangle 2
A_2=1/2( 10)( 4)
A_2=20mi^2
The area of the top triangle is 35 square miles and the area of the bottom triangle is 20 square miles. Finally, let's add both areas to find the total area of the trapezoid.
Area of the Trapezoid
35+ 20=55mi^2
