Geometry

Question Analysis

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

 

Key Concept Explanation

The area  of a trapezoid is given by the formula , where  and  are the lengths of the two bases and  is the height. This formula is derived from 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 right side of the trapezoid, the hypotenuse is  and the base is . According to the Pythagorean theorem  (where  is the hypotenuse and  and  are the other two sides), the height  of the trapezoid is .

2. Identify the base lengths:

The lengths of the bases are

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