Question

the area of a parallelogram is 16 square units. one side of the parallelogram is 10 units long. the other side is 20 units long. determine whether each statement is true. select true or false for each statement. the height of the parallelogram could be 0.5 unit because 20×0.5 = 10. the height of the parallelogram could be 0.8 unit because 20×0.8 = 16. the height of the parallelogram could be 1.25 units because 16×1.25 = 20. the height of the parallelogram could be 1.6 units because 10×1.6 = 16.

Explanation:

Step1: Recall area formula

The area formula of a parallelogram is $A = base\times height$.

Step2: Check first statement

If base $b = 20$ and height $h=0.5$, then $A=b\times h=20\times0.5 = 10
eq16$. So it's false.

Step3: Check second statement

If base $b = 20$ and height $h = 0.8$, then $A=b\times h=20\times0.8=16$. So it's true.

Step4: Check third statement

The area formula is $A = base\times height$, not $base=area\times height$. If we assume base - height relationship for area 16, this statement's logic is wrong. So it's false.

Step5: Check fourth statement

If base $b = 10$ and height $h=1.6$, then $A=b\times h=10\times1.6 = 16$. So it's true.

Answer:

1. False
2. True
3. False
4. True