Ø What is the effect on the area of a triangle if the base is doubled and the height is cut in half? What happens to the area, if the base is doubled and the height remains the same?
To determine the effects on the area of a triangle when the base is doubled and the height is cut in half, we will use the formula for the area of a triangle:
Area = (base * height) / 2
1. If the base is doubled and the height is cut in half:
Let's say the original base is 'b' and the original height is 'h'.
The area of the original triangle is: Area = (b * h) / 2
When the base is doubled, the new base becomes '2b'.
When the height is cut in half, the new height becomes 'h/2'.
So, the new area of the triangle would be: New Area = (2b * (h/2)) / 2
Simplifying this equation: New Area = (2bh) / 4
Now, we can further simplify the equation by canceling out the common factor '2'. The equation becomes: New Area = (bh) / 2
This means that when you double the base and cut the height in half, the area of the triangle is reduced to half of its original area.
2. If the base is doubled and the height remains the same:
Following the same logic, let's say the original base is 'b' and the original height is 'h'.
The area of the original triangle is: Area = (b * h) / 2
When the base is doubled, the new base becomes '2b'.
So, the new area of the triangle would be: New Area = (2b * h) / 2
Simplifying this equation: New Area = bh
This means that when you double the base and keep the height the same, the area of the triangle is also doubled.
In summary:
- If the base is doubled and the height is cut in half, the area of the triangle is reduced to half of its original area.
- If the base is doubled and the height remains the same, the area of the triangle is doubled.