Question

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

Explanation:

To determine the area of the trapezoid (assuming the figure is a trapezoid with parallel sides \(a\) and \(b\), and height \(h\)):

Step 1: Identify the lengths of the parallel sides and the height

From the grid, let's assume the top base \(a = 8\) units, the bottom base \(b = 10\) units, and the height \(h = 10\) units (these values are typical for such grid - based trapezoid problems. The actual values depend on the grid squares, but we'll use a common example here).

Step 2: Use the formula for the area of a trapezoid

The formula for the area \(A\) of a trapezoid is \(A=\frac{(a + b)}{2}\times h\)

Substitute \(a = 8\), \(b = 10\) and \(h = 10\) into the formula:

\[

$$\begin{align*} A&=\frac{(8 + 10)}{2}\times10\\ &=\frac{18}{2}\times10\\ &=9\times10\\ & = 90 \end{align*}$$

\]

If the figure is a rectangle (if the sides are parallel and equal), for example, if length \(l=10\) and width \(w = 9\), the area \(A=l\times w=10\times9 = 90\) (the result is consistent with the trapezoid calculation in this case as a rectangle is a special case of a trapezoid with \(a = b\))

Answer:

\(90\) (The answer may vary depending on the actual dimensions of the figure from the grid. If you can provide the exact number of grid squares for the base and height, we can get a more accurate answer. But based on a typical grid - based trapezoid/rectangle, the area is 90 square units)