The area of a triangle is 124 square units. What would its new area be if its base was half as long, and its height was three times as long?
Write in your own words showing the math steps.
To find the new area of the triangle, we first need to calculate the new base and height of the triangle.
Let the original base be denoted as b and the original height be denoted as h.
Given that the area of the original triangle is 124 square units, we have:
Area = (1/2) * base * height
124 = (1/2) * b * h
Next, we are told that the new base is half as long as the original base, so the new base is b/2. Additionally, the new height is three times as long as the original height, so the new height is 3h.
Therefore, the new area of the triangle can be calculated using the formula for the area of a triangle:
New Area = (1/2) * new base * new height
New Area = (1/2) * (b/2) * (3h)
New Area = (1/4) * b * 3h
Substitute the expression for the original area (124) into this equation:
New Area = (1/4) * 124
New Area = 31
Therefore, the new area of the triangle would be 31 square units.