The area of a triangle is 132 square units. What would its new area be if its base was half as long and its height was three times as long? Please show all work to receive full credit.
Let the original base of the triangle be x units and the original height be y units.
The original area of the triangle is given by the formula:
Area = 1/2 * base * height
132 = 1/2 * x * y
264 = x * y (equation 1)
Now, the new base is half as long, so it is x/2 units.
The new height is three times as long, so it is 3y units.
The new area of the triangle is given by the formula:
New Area = 1/2 * new base * new height
New Area = 1/2 * (x/2) * (3y)
New Area = 1/4 * x * 3y
New Area = 3/4 * x * y (equation 2)
Substitute equation 1 into equation 2:
New Area = 3/4 * 264
New Area = 198
Therefore, the new area of the triangle would be 198 square units.