A trapezoid is a four-sided shape (quadrilateral) with at least one pair of parallel sides. These parallel sides are called bases (base 1 and base 2). The height of the trapezoid is the perpendicular distance between these bases. To find the area of a trapezoid, you need to know the lengths of both bases and the height.
The formula for the area of a trapezoid is given by: $A = \frac{1}{2}h(b_1 + b_2)$, where $A$ is the area, $h$ is the height, $b_1$ is the length of base 1, and $b_2$ is the length of base 2. Essentially, you're averaging the lengths of the two bases and then multiplying by the height.
Match each term with its definition:
| Term | Definition |
|---|---|
| 1. Base 1 | A. The perpendicular distance between the bases |
| 2. Base 2 | B. The area enclosed within the trapezoid |
| 3. Height | C. One of the parallel sides of the trapezoid |
| 4. Area | D. The other parallel side of the trapezoid |
| 5. Trapezoid | E. A quadrilateral with at least one pair of parallel sides |
A trapezoid is a quadrilateral with at least one pair of __________ sides. These sides are called __________ and __________. The __________ is the perpendicular distance between the bases. The formula to calculate the __________ of a trapezoid is $A = \frac{1}{2}h(b_1 + b_2)$.
Explain, in your own words, why we average the lengths of the bases when calculating the area of a trapezoid. How does this relate to finding the area of a rectangle or parallelogram?
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