Question

what is the area of the figure shown? the area is □ 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 $A=\frac{(b_1 + b_2)h}{2}$, 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, let's assume the top base $b_1 = 7$ units, the bottom base $b_2 = 9$ units, and the height $h = 8$ units (by counting the grid squares).

Step3: Apply the trapezoid area formula

Substitute the values into the formula: $A=\frac{(7 + 9)\times8}{2}$. First, calculate the sum of the bases: $7 + 9 = 16$. Then multiply by the height: $16\times8 = 128$. Finally, divide by 2: $\frac{128}{2}=64$.

Answer:

64