A parallelogram has an area of 42 cm?. What would the area be if the base was one-third as long and the height was twice as long?

Let the original base of the parallelogram be represented by b and the original height be represented by h.

Given that the original area is 42 cm², we have:

Area = base x height
42 = b x h

If the base is one-third as long as the original base, then the new base would be b/3. If the height is twice as long as the original height, then the new height would be 2h.

The new area would be:

New area = new base x new height
= (b/3) x (2h)
= (2/3)bh

Since 42 = bh, we can substitute this into the equation for the new area:

New area = (2/3)(42)
= 28 cm²

Therefore, if the base is one-third as long and the height is twice as long, the area would be 28 cm².