(1/2)b*hAstronuc said:What is the formula for the area of a triangle, if one is given base and height?
Has one done the cross product of two vectors?
Astronuc said:Nevermind the cross-product. I was thinking that you had to find the area of the triangle. In future, please write out the problem statement in the post, rather than leaving it as a image.
Anyway, so we have A = 1/2 bh, as the area. Now if we take the line segment AB as the base, b, which is fixed, then what does h represent with respect to point C? And if the area, A, and base, b, remain constant, what does that imply about point C with respect to line segment AB?
Alright, I get it now. Thank you both for the help.HallsofIvy said:Take AB as the base. As C moves, A and B stay fixed so b stays constant. In order that the area be constant, h must also be constant. That means C must move along a line parallel to AB.
The formula for finding the area of a triangle is A = 1/2 * b * h, where A is the area, b is the base length, and h is the height.
The base and height of a triangle can be determined by measuring the lengths of its sides and using the Pythagorean theorem to calculate the missing side, or by using trigonometric functions to calculate the angles and then using trigonometric ratios to find the base and height.
No, the area of a triangle cannot be negative since it represents a physical quantity and cannot have a negative value.
Yes, there are special cases when calculating the area of a triangle such as when the triangle is a right triangle, in which case the formula becomes A = 1/2 * b * h, where b and h are the lengths of the two legs, or when the triangle is an equilateral triangle, in which case the formula becomes A = (√3/4) * s^2, where s is the length of one side.
Yes, the area of a triangle can be calculated if only the lengths of the sides are known by using Heron's formula, which states that A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter of the triangle and a, b, and c are the lengths of the sides.