Find the area of the trapezoid.
Find the area of the trapezoid.
The Correct Answer and Explanation is:
To find the area of a trapezoid, we use the area formula for a trapezoid:Area=12×(b1+b2)×h\text{Area} = \frac{1}{2} \times (b_1 + b_2) \times hArea=21×(b1+b2)×h
Where:
- b1b_1b1 = length of the first base
- b2b_2b2 = length of the second base
- hhh = height (the perpendicular distance between the two bases)
Since you didn’t provide specific values, here’s a general explanation and example:
Let’s assume:
- b1=8b_1 = 8b1=8 units
- b2=5b_2 = 5b2=5 units
- h=4h = 4h=4 units
Then the area is:Area=12×(8+5)×4=12×13×4=522=26 square units\text{Area} = \frac{1}{2} \times (8 + 5) \times 4 = \frac{1}{2} \times 13 \times 4 = \frac{52}{2} = 26 \text{ square units}Area=21×(8+5)×4=21×13×4=252=26 square units
Explanation:
A trapezoid (also called a trapezium in some countries) is a quadrilateral with exactly one pair of parallel sides. These parallel sides are referred to as the bases of the trapezoid. The non-parallel sides are called the legs. To find the area of a trapezoid, we need the lengths of the two bases and the height—the perpendicular distance between them.
The area formula, 12×(b1+b2)×h\frac{1}{2} \times (b_1 + b_2) \times h21×(b1+b2)×h, is essentially an average of the two base lengths multiplied by the height. You can think of it as taking the average length of the bases and then stretching that over the height. This formula makes sense because the trapezoid can be thought of as a shape between a rectangle and a triangle.
Let’s consider the reason behind this formula. A rectangle has a constant width, so its area is simply base times height. A triangle, on the other hand, tapers to a point, so its area is half the base times the height. A trapezoid is like a rectangle with one base shorter or longer, giving a weighted average between the two.
In real-life applications, trapezoids often appear in architecture, land plotting, and graphic design. Calculating the area accurately is crucial for tasks like determining floor area or materials needed.
