Geometry

Question Analysis

The main focus is on using the formula for the area of a trapezoid to find the unknown height. Given the area and the lengths of the two bases,  we need to re - arrange the formula to solve for the height.

Key Concept Explanation

The area  of a trapezoid is calculated by the formula , where  and  are the lengths of the bases and  is the height. To find , we can re - arrange the formula as  through algebraic manipulation. This is based on the principle of isolating the variable  in the original area formula.

Step - by - Step Solution

1. Identify the re - arranged formula:

We use the formula .

2. Substitute the given values:

Given , , and .

First, find the sum of the bases:

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