Question

what is the area of the figure shown? the area is \\( \square \\) square units. (type an integer or a simplified fraction.)

Explanation:

Step1: Identify the figure type

The figure is a trapezoid. The formula for the area of a trapezoid is $A = \frac{1}{2}(b_1 + b_2)h$, where $b_1$ and $b_2$ are the lengths of the two parallel sides (bases), and $h$ is the height (the perpendicular distance between the bases).

Step2: Determine the lengths of the bases and the height

From the grid:

• The length of the longer base ($b_1$): Let's count the grid units. It spans 10 units (from leftmost to rightmost point of the lower base).
• The length of the shorter base ($b_2$): It spans 2 units (the top base).
• The height ($h$): The vertical distance between the two bases. Looking at the grid, it is 2 units (from the top base to the bottom base, counting the vertical grid lines).

Step3: Apply the trapezoid area formula

Substitute $b_1 = 10$, $b_2 = 2$, and $h = 2$ into the formula:

$$\begin{align*} A&=\frac{1}{2}(10 + 2)\times2\\ &=\frac{1}{2}(12)\times2\\ &= 6\times2\\ &= 12 \end{align*}$$

Answer:

12