Question

the line segment shown on the grid is the base of a parallelogram. use the polygon tool to draw a non - rectangular parallelogram with an area of 20 square units that includes the given base. to use the polygon tool, click on each vertex of the parallelogram, starting and ending at the same point. it will turn blue when complete.

Explanation:

Step1: Determine the base length

First, we need to find the length of the given base. Looking at the grid, if we assume each grid square has a side length of 1 unit, we can count the number of units between the two endpoints of the base. Let's say the base length \( b \) is 5 units (for example, if the two endpoints are 5 grid units apart horizontally).

Step2: Recall the area formula for a parallelogram

The area \( A \) of a parallelogram is given by the formula \( A = b \times h \), where \( b \) is the base length and \( h \) is the height (the perpendicular distance between the base and the opposite side).

Step3: Calculate the required height

We know the area \( A = 20 \) square units and we found the base \( b = 5 \) units. Using the formula \( A = b \times h \), we can solve for \( h \):

$$ 20 = 5 \times h $$

Dividing both sides by 5, we get:

$$ h = \frac{20}{5} = 4 $$

So the height needs to be 4 units.

Step4: Draw the parallelogram

Starting from one endpoint of the base, move up (or down, but not vertically to avoid a rectangle) 4 units (in the direction perpendicular to the base) to get the third vertex. Then move the same distance as the base length from this third vertex to get the fourth vertex, and finally connect back to the starting point. For example, if the base is from \( (x_1, y_1) \) to \( (x_2, y_2) \) (where \( x_2 - x_1 = 5 \) and \( y_1 = y_2 \)), then the third vertex could be \( (x_1, y_1 + 4) \) and the fourth vertex would be \( (x_2, y_2 + 4) \). Connecting these four points in order (and back to the start) will form the non - rectangular parallelogram with area 20 square units.

Answer:

To draw the non - rectangular parallelogram:

1. Identify the length of the given base (e.g., if it spans 5 grid units horizontally).
2. Calculate the height as \( h=\frac{20}{5} = 4\) units using the parallelogram area formula \( A = b\times h\).
3. From one end of the base, move 4 units perpendicular to the base (not vertically to avoid a rectangle) to get a new vertex.
4. Move the same length as the base from this new vertex to get the fourth vertex.
5. Connect the four vertices (starting and ending at the same point) using the Polygon tool.