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 each figure

1. Check if opposite sides are parallel.
2. For non - parallelograms, note the non - parallel sides.

Step3: Calculate area of parallelograms

Use formula \(A = base\times height\). Count grid squares for base and height.

Answer:

1. Parallelogram (Yes). Opposite sides are parallel.
2. Parallelogram (Yes). Opposite sides are parallel.
3. Parallelogram (Yes). Opposite sides are parallel (it's a rectangle, a special parallelogram).
4. Not a parallelogram. Opposite sides are not parallel.
5. Area: Count base and height in grid squares. If base \(b = 4\) cm and height \(h=2\) cm, \(A=b\times h = 4\times2=8\) \(cm^{2}\).
6. Area: If base \(b = 3\) cm and height \(h = 3\) cm, \(A=b\times h=3\times3 = 9\) \(cm^{2}\).
7. Area: If base \(b=5\) cm and height \(h = 2\) cm, \(A=b\times h=5\times2 = 10\) \(cm^{2}\).