What is the area, in square meters, of the trapezoid with a top base of 13.1m, a bottom base of 7.4m and a height of 8m?

Steps to Solve

1. Recall 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 two bases (the parallel sides) and $h$ is the height (the perpendicular distance between the bases).

2. Identify the values of $b_1$, $b_2$, and $h$ from the given information

From the image, we have: $b_1 = 13.1$ meters $b_2 = 7.4$ meters $h = 8$ meters

3. Substitute the values into the formula and calculate the area

Substitute the values of $b_1$, $b_2$, and $h$ into the area formula:

$$ A = \frac{1}{2}(13.1 + 7.4)(8) $$

4. Simplify the expression

First, add the lengths of the bases: $13.1 + 7.4 = 20.5$

Now, substitute this back into the formula: $$ A = \frac{1}{2}(20.5)(8) $$

Multiply $20.5$ by $8$: $20.5 \times 8 = 164$

Finally, multiply by $\frac{1}{2}$ (or divide by 2): $$ A = \frac{1}{2} \times 164 = 82 $$

The area of the trapezoid is 82 square meters.