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.