Question

activity 2 name: more parallelograms 7 which parallelogram has a greater area? use as few measurements as you can to help you decide. a b they have the same area. show or explain your thinking.

Explanation:

Step1: Recall area formula for parallelogram

The area formula for a parallelogram is $A = base\times height$, where the height is the perpendicular - distance between the base and the opposite side.

Step2: Identify base and height for parallelogram A

For parallelogram A, if we consider the base as $7.3$ cm and the height as $7$ cm, then the area $A_A=7.3\times7 = 51.1$ $cm^2$.

Step3: Identify base and height for parallelogram B

For parallelogram B, assume the base is the side parallel to the given side of length $8$ cm. Since the two parallelograms share the same vertical distance (height) between the parallel - lines that contain their bases, and if we consider the relationship between the sides and the fact that the height with respect to the base of parallelogram B is also $7$ cm (because of the parallel - line setup), and assume the base of parallelogram B is $b$. But we can also use the fact that the area of parallelogram B with base $b$ and height $h = 7$ cm. The area of parallelogram B is also calculated using the formula $A = base\times height$. If we consider the non - perpendicular side lengths, we note that the vertical height between the parallel sides of both parallelograms is the same. Since the perpendicular height from the base to the opposite side is the same for both parallelograms (because they are between the same parallel lines), and if we assume the base of parallelogram B such that the height is $7$ cm, and using the fact that the area formula $A = base\times height$, we can see that if we consider the base of parallelogram B as $b$ and height $h = 7$ cm, and since the vertical distance between the parallel sides is the same for both, and the area of parallelogram A with base $7.3$ cm and height $7$ cm and parallelogram B with appropriate base and the same height, we find that they have the same area.

Answer:

They have the same area.