Answer:
The area of the trapezoid is 15 square miles.
Step-by-step explanation:
There are two ways you can solve for the area of a trapezoid.
The first way is to memorize the formula for a trapezoid:
[tex]A = \frac{1}{2} (b_{1} + b_{2} )h\\[/tex]
where b1 and b2 are the bases of the trapezoid;
h is the height of the trapezoid.
Simply substitute the values you have from the problem. b1 is 2 miles, b2 is 3 miles, and h is 6 miles.
(Note that b1 and b2 are interchangeable, so do not worry about which value for a base of the trapezoid should be b1 or b2.)
[tex]A = \frac{1}{2} (b_{1} + b_{2} )h\\[/tex]
A = (1/2)*(2mi + 3mi)*(6mi)
Simplify.
A = (3mi)(5mi) = 15 sqare miles
The second way is to split the area of the trapezoid into smaller areas. We know that this trapezoid is made up of two triangles and a rectangle. So let it be that! The area of the trapezoid is the area of the two triangles plus the area of the rectangle.
A = 2*(1/2)(b)(h) + (b)(h)
The base of the triangle is 1/2 mile and the height of the triangle is 6 miles. The base of the rectangle is 2 miles and the height of the rectangles is 6 miles.
A = 2*(1/2)*(1/2mi)*(6mi) + (2mi)(6mi)
Simplify.
A = 3 square miles + 12 square miles = 15 square miles.
