A triangle with an area of 25 square units is rotated 180 degrees clockwise. What is the area of the rotated figure
The area of the rotated figure is still 25 square units because rotation preserves area.
To find the area of the rotated triangle, we need to calculate the area of the original triangle first.
Let's assume the original triangle has a base length of 'b' units and a height of 'h' units.
The area of a triangle is given by the formula: Area = (base * height) / 2
We are given that the area of the original triangle is 25 square units, so we can write the equation as: 25 = (b * h) / 2
Simplifying the equation: 50 = b * h
Now, when the triangle is rotated 180 degrees clockwise, the base becomes the height, and the height becomes the base.
So for the rotated triangle, the new base length will be 'h' units and the new height will be 'b' units.
The formula for the area of the rotated triangle will be: Area_rotated = (base_rotated * height_rotated) / 2
Substituting the new base and height values, we get: Area_rotated = (h * b) / 2
Since we know that the area of the rotated triangle is the same as the original triangle (25 square units), we have: (h * b) / 2 = 25
Multiplying both sides of the equation by 2, we get: h * b = 50
This equation gives us the area of the rotated triangle as well: Area_rotated = 25 square units.
Therefore, the area of the rotated figure is also 25 square units.