We want to find a formula for the area A of the trapezoid. To do so, notice that we can divide the trapezoid into three figures: two triangles and one rectangle.
This means that we can calculate the area of each figure and then add them to obtain the area of the trapezoid. Let's do one at time!
Area of the First Triangle
Consider that the base of the triangle is equal to a_1 and the height is h.
In this case, let's consider the base of the second triangle as a_2.
Again, we will use the known formula for the area of a triangle.
A_2= a_2 * h/2
Area of Rectangle
Finally, we will calculate the area of the rectangle. We can name the base b_1 and the height h.
Recall the formula for a rectangle.
A_3= b_1 * h
Finding the Area of the Trapezoid
The area of the trapezoid is equal to the sum of the areas of the two triangles and the area of the rectangle.
A=A_1+A_2+A_3
We will substitute the obtained areas into this equation and simplify it. Let's do it!
Now, we will assume that the longer base of the trapezoid is b_2. The longer base is the sum of the base of the rectangle and the base of each triangle.
b_2 = a_1+ a_2 + b_1
Let's use this to continue simplifying the obtained equation for the area of the trapezoid
We want to find the value of h. To do so, we can use the formula obtained in Part A.
A=1/2h(b_1+b_2)
We will use inverse operations to isolate the variable h on one side of the formula.
