Geometry
Question

What is the area of the trapezoid?
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Answer & Analysis
Answer
Analysis
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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