Question

find the area of this trapezoid.
\\(h = 4\text{ m}\\)
\\(b_1 = 6\text{ m}\\)
\\(b_2 = 9\text{ m}\\)
\\(c = d = 6\text{ m}\\)

Explanation:

🆕 New Concept Discovered: Area of a Trapezoid
Average the parallel bases, then multiply by height

Step 1: Identify the formula

To find the area of a trapezoid, we use the formula:

$$ A = \frac{b_1 + b_2}{2} \cdot h $$

This formula means we take the average length of the two parallel bases (\(b_1\) and \(b_2\)) and multiply it by the perpendicular height (\(h\)). The slanted side lengths (\(c\) and \(d\)) are extra information and are not needed to calculate the area.

Step 2: Substitute the given values

From the problem, we have:

• \(b_1 = 6\text{ m}\)
• \(b_2 = 9\text{ m}\)
• \(h = 4\text{ m}\)

Substitute these values into the formula:

$$ A = \frac{6 + 9}{2} \cdot 4 $$

Step 3: Calculate the final area

First, add the bases inside the parentheses:

$$ 6 + 9 = 15 $$

Next, divide by \(2\) to find the average base length:

$$ \frac{15}{2} = 7.5 $$

Finally, multiply by the height:

$$ A = 7.5 \cdot 4 = 30 $$

Answer:

30