the area of a triangle is 124 square units what would it’s new area be if it’s base was half as long and its height was three times as long

1 answer

If the base of the triangle is halved and the height is tripled, the new area of the triangle can be calculated using the formula for the area of a triangle:

Area = (1/2) * base * height

Let the original base be "b" units and original height be "h" units. The original area of the triangle is given as 124 square units.

Therefore, 124 = (1/2) * b * h

Now, new base = b/2 and new height = 3h. The new area of the triangle can be calculated as:

New Area = (1/2) * (b/2) * (3h)
= (1/2) * (3/2) * b * h
= (3/4) * b * h

Since the original area was 124 square units, we have:

124 = (3/4) * b * h

Now, to find the new area with the halved base and tripled height, plug in the values into the equation:

New Area = (3/4) * (b/2) * (3h)
= (3/4) * (1/2) * b * 3h
= (3/8) * b * 3h
= (9/8) * b * h

Therefore, the new area of the triangle with a base that is half as long and a height that is three times as long would be 9/8 times the original area.

(9/8) * 124 = 139.5 square units

So, the new area of the triangle would be 139.5 square units.