What is the area of a right trapezoid with bases of 15 yards and 25 yards, and a height of 18 yards?
Understand the Problem
The question asks to find the area of a right trapezoid given the lengths of its bases and its height. The area of a trapezoid can be calculated using the formula: Area = (1/2) * (base1 + base2) * height.
Answer
$A = 24$
Answer for screen readers
$A = 24$
Steps to Solve
- Write down the formula for the area of a trapezoid
The area $A$ of a trapezoid is given by the formula:
$$ A = \frac{1}{2} (b_1 + b_2)h $$
where $b_1$ and $b_2$ are the lengths of the bases and $h$ is the height.
- Identify the given values
From the problem, we have: $b_1 = 10$, $b_2 = 14$, and $h = 2$
- Substitute the values into the formula
Substitute the given values into the area formula:
$$ A = \frac{1}{2} (10 + 14) \cdot 2 $$
- Simplify the expression
First, add the lengths of the bases:
$$ A = \frac{1}{2} (24) \cdot 2 $$
Next, multiply by $\frac{1}{2}$ and 2, which cancel each other out:
$$ A = 24 $$
$A = 24$
More Information
The area of the right trapezoid is 24 square units. Since no specific units were given (e.g., cm, inches), we express the answer in generic "square units".
Tips
A common mistake is to confuse the height with the length of the slanted side of the trapezoid. It is important to correctly identify the height as the perpendicular distance between the two bases. Another common mistake is using the wrong formula, such as the formula for the area of a parallelogram or triangle.
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