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 rearrange 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. By rearranging this formula through algebraic operations, we get , which allows us to find the height when the area and bases are known.

Step - by - Step Solution

1. Identify the formula for the height:

Use the formula .

2. Substitute the given values:

Given , , and .

First, calculate the sum of the bases: