Question

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?

Answer 1

Area of a parallelogram is the product of its base and height.

Let the base be "b" and height be "h". So we can write:

Area  = bh = 42 cm²

After the change, base is one-third. So the new length of the base will be: b/3 
After the change, height is twice as long. So the new height will be :  2h

Area after the change = $\frac{b}{3}* 2h= \frac{2}{3} bh$
Using the value of bh from equation above we get:

Area after the change = $\frac{2}{3} * 42 = 28$ cm²

So the area of new parallelogram will be 28 cm²