How to find the height of a trapezoid?
Understand the Problem
The question is asking how to calculate the height of a trapezoid, which is a geometric shape. The height can typically be determined using the formula involving the lengths of the bases and area, or using trigonometric relationships if angles are known.
Answer
h = \frac{2A}{a + b}
Answer for screen readers
The height of the trapezoid can be found using the formula $h = \frac{2A}{a + b}$ where A is the area and a and b are the lengths of the bases.
Steps to Solve
- Identify the formula for the height of a trapezoid
The height (h) of a trapezoid can be found using the area (A) and the lengths of the two bases (a and b) with the formula:
$$A = \frac{1}{2} \times (a + b) \times h$$
- Rearrange the formula to solve for height (h)
To isolate h, we rearrange the formula:
$$h = \frac{2A}{a + b}$$
- Insert the known values into the formula
Plug in the values for the area (A) and the lengths of the bases (a and b):
$$h = \frac{2A}{a + b}$$
For example, if a trapezoid has an area of 40 square units, base lengths of 5 units and 7 units respectively, the height would be:
$$h = \frac{2 \times 40}{5 + 7} = \frac{80}{12} \approx 6.67$$
The height of the trapezoid can be found using the formula $h = \frac{2A}{a + b}$ where A is the area and a and b are the lengths of the bases.
More Information
The height of a trapezoid can be calculated using the area and the lengths of the bases. This formula is very useful in geometry.
Tips
A common mistake is not correctly rearranging the formula or forgetting to multiply the area by 2. Always double-check your work for arithmetic errors.
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