A parallelogram has an area of 42cm^2. What would the area be if the base was one-third as long and the height was twice as long?
To find the area of the new parallelogram with the adjusted base and height, we can use the formula for the area of a parallelogram: A = base x height.
Let the original base be b and the original height be h. So, the original area is 42cm^2: 42 = b x h.
Now, the new base is one-third as long as the original base, so the new base is b/3.
The new height is twice as long as the original height, so the new height is 2h.
Therefore, the area of the new parallelogram is: A = (b/3) x (2h) = (2b/3) x h.
Since we know that the original area is 42cm^2, we can substitute this into the equation: 42 = (2b/3) x h.
Solving for the new area:
42 = (2b/3) x h
42 = (2b x h) / 3
42 = 42
So the new area of the parallelogram with the adjusted base and height would also be 42cm^2.