Geometry

Question Analysis

The main focus is on applying the formula for the area of a trapezoid. First, we need to find the height of the trapezoid using the right - angled triangle on the left side, and then calculate the area with the known base lengths.

 

Key Concept Explanation

The area  of a trapezoid is calculated by the formula , where  and  are the lengths of the two bases and  is the height. This formula is based on combining two congruent trapezoids to form a parallelogram and taking half of its area.

 

Step - by - Step Solution

1. Find the height of the trapezoid:

In the right - angled triangle on the left side, with hypotenuse  and base . By the Pythagorean theorem , the height .

2. Identify the base lengths:

The bases are  and

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