- #1
Monoxdifly
MHB
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Klaas van Aarsen said:Hi Mr. Fly,
How about a tight rectangle around the triangle and estimate its side lenghts?
The area of the triangle is then the area of the rectangle minus the area of the three right triangles.
Monoxdifly said:But the vertices of the triangle don't even touch the rectangle, so I think it's not that easy.
To find the area of a triangle with non-intersecting vertices using the Pythagorean theorem, you will need to know the lengths of all three sides of the triangle. Once you have the lengths, you can use the formula A = 1/2 * base * height, where the base is one of the sides and the height is the perpendicular distance from that side to the opposite vertex. You can then use the Pythagorean theorem (a² + b² = c²) to find the height, and plug it into the formula to calculate the area.
Yes, you can use the Heron's formula to find the area of a triangle with non-intersecting vertices. This formula is especially useful when you do not know the lengths of all three sides of the triangle. The formula is A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter (half of the perimeter) and a, b, and c are the lengths of the sides. This formula works for all types of triangles, including those with non-intersecting vertices.
The base of a triangle with non-intersecting vertices is one of the sides of the triangle, while the height is the perpendicular distance from that side to the opposite vertex. The base and height are always perpendicular to each other, and they form a right triangle with one of the sides of the triangle. The base and height are essential in calculating the area of a triangle using the formula A = 1/2 * base * height.
If you only know the coordinates of the vertices, you can use the formula A = 1/2 * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)| to find the area of the triangle. In this formula, (x1, y1), (x2, y2), and (x3, y3) are the coordinates of the three vertices. This formula is derived from the cross-product of two vectors and works for all types of triangles, including those with non-intersecting vertices.
Yes, you can use trigonometry to find the area of a triangle with non-intersecting vertices. You will need to know the lengths of at least two sides and the angle between them. You can then use the formula A = 1/2 * a * b * sin(C), where a and b are the lengths of the two sides and C is the angle between them. This formula is derived from the formula for the area of a parallelogram and works for all types of triangles, including those with non-intersecting vertices.