A portion of a rectangle is shaded as shown. The area of the shaded region is 78 in.2. What is the value of x? Show your work.

Solution:

Finding the area of the large rectangle.

We know that:

This means that we got two ways to find the area of the triangle.

Those methods are:

Let's put these two methods in an equation as both are equal.

Substituting the base of the triangle:

Simplifying the RHS:

Simplifying the LHS:

Dividing 6 both sides:

Since the height is 3 in, the measure of x is 5 in because the sum of the height and x must be 8.

multiplication is multiplication.   it might feel harder depending on what level of math you are in, but generally it will be the same old stuff, while implementing some new concepts and methods of solving work.