Question

draw a new parallelogram with the same base and a different height. use the original parallelograms area formula correctly.

Explanation:

Step1: Recall area formula for parallelogram

The area formula of a parallelogram is $A = b\times h$, where $b$ is the base and $h$ is the height. For the original parallelogram, with base $b_1 = 6$ cm and height $h_1= 8$ cm, the area $A_1$ is calculated as $A_1=b_1\times h_1$.
$A_1 = 6\times8=48$ $cm^{2}$.

Step2: Determine new - height condition

We want to draw a new parallelogram with the same base ($b_2 = 6$ cm) and an area that is 40 square centimeters less than the original. The new area $A_2$ is $A_2=A_1 - 40$. So $A_2=48 - 40=8$ $cm^{2}$.

Step3: Calculate new height

Using the area formula $A = b\times h$ again, with $A = A_2 = 8$ $cm^{2}$ and $b = b_2=6$ cm, we can solve for the new height $h_2$. Rearranging the formula gives $h_2=\frac{A_2}{b_2}$.
$h_2=\frac{8}{6}=\frac{4}{3}\approx1.33$ cm.

To draw the new parallelogram:

1. Draw a base of length 6 cm.
2. Using a set - square or other right - angle tool, draw a perpendicular line segment of length $\frac{4}{3}$ cm at one of the endpoints of the base.
3. Draw a line parallel to the base through the top - end of the perpendicular line segment.
4. Mark a point on this parallel line such that the distance along the parallel line from the starting point (above the base) is 6 cm.
5. Connect the endpoints to form the new parallelogram.

Answer:

The height of the new parallelogram is $\frac{4}{3}$ cm. Draw a parallelogram with a base of 6 cm and a height of $\frac{4}{3}$ cm following the steps above.