Question

problems 1 - 4: determine whether each figure is a parallelogram. for figures that are not parallelograms, explain how you know.
problems 5 - 7: use any strategy to determine the area of the parallelograms.

Explanation:

Step1: Recall parallelogram definition

A parallelogram has two pairs of parallel sides.

Step2: Analyze Figure 1

The top and bottom sides are not parallel. So it's not a parallelogram.

Step3: Analyze Figure 2

It has two pairs of parallel sides. So it's a parallelogram.

Step4: Analyze Figure 3

It has two pairs of parallel sides (a rectangle is a special - type of parallelogram). So it's a parallelogram.

Step5: Analyze Figure 4

It has only one pair of parallel sides. So it's not a parallelogram.

Answer:

1. No, top and bottom sides are not parallel.
2. Yes
3. Yes
4. No, only one pair of parallel sides.

For problems 5 - 7, the area of a parallelogram is given by \(A = b\times h\) (base times height).

Step1: For Figure 5

Count the base and height along the grid. Let's say the base \(b = 5\) cm and height \(h=3\) cm. Then \(A = 5\times3=15\) \(cm^{2}\).

Step2: For Figure 6

Count the base and height. Suppose base \(b = 4\) cm and height \(h = 4\) cm. Then \(A=4\times4 = 16\) \(cm^{2}\).

Step3: For Figure 7

Count the base and height. If base \(b=3\) cm and height \(h = 5\) cm. Then \(A=3\times5=15\) \(cm^{2}\).