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If the base of a triangle is increased by 10% and the Altitude is decreased by 10% then the new Area of the Triangle
The new area is decreased by 1%.
To find the new area of the triangle after increasing the base by 10% and decreasing the altitude by 10%, we’ll use the formula for the area of a triangle: Area = (1/2) * base * altitude.
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Let’s assume the original base of the triangle is ‘b’ and the original altitude is ‘h’.
After increasing the base by 10%, the new base will be 1.1b (since increasing by 10% means adding 10% of the original value). After decreasing the altitude by 10%, the new altitude will be 0.9h (since decreasing by 10% means subtracting 10% of the original value).
Therefore, the new area of the triangle will be:
New Area = (1/2) * (1.1b) * (0.9h)
New Area = (1/2) * 1.1 * 0.9 * b * h
New Area = 0.99 * (1/2) * b * h
New Area = 0.99 * Original Area
This means that the new area will be 99% of the original area. So, the new area is decreased by 1%.
Area and Perimeter of a Triangle
The area A of a triangle can be calculated using various methods, but one common formula is:
A = (1/2) * base * height
where the base is the length of one side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex.
The perimeter P of a triangle is the sum of the lengths of its three sides. If the lengths of the sides are a, b, and c, then the perimeter P is given by:
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P = a + b + c
These formulas can be applied to any triangle, whether it’s equilateral, isosceles, or scalene. Just make sure you have the necessary side lengths and height to calculate the area, and the lengths of all three sides to calculate the perimeter.
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Source: Math Hello Kitty
Categories: Math
