- #1
Can area of a triangle be 0.5(c x a) instead of 0.5(a x c)?
In summary, the conversation discusses using the magnitude of the cross-product of two vectors to find the area of a triangle. It is mentioned that the direction of the cross-product does not matter as long as the magnitude is the same.
- #2
Millennial
- 296
- 0
[itex]ca = ac[/itex], so yes.
- #3
coolul007
Gold Member
- 271
- 8
Not in that figure, unless angle B is 90 degrees.
- #4
- #5
mark.watson
- 14
- 2
mark.watson said:
I didn't see the second part of your question. The direction of ||A x C|| or ||C x A|| doesn't matter because they have the same magnitude. That is why (1/2)||A x C|| = (1/2)||C x A|| is true.
- #6
coconut62
- 161
- 1
Thank you very much.
FAQ: Can area of a triangle be 0.5(c x a) instead of 0.5(a x c)?
Can the formula for the area of a triangle be written as 0.5(c x a) instead of 0.5(a x c)?
Yes, the formula for the area of a triangle can be written as 0.5(c x a) instead of 0.5(a x c). This is because the order of the sides does not affect the result as long as they are multiplied together.
Why is the area of a triangle divided by 2?
The area of a triangle is divided by 2 because it is half of the area of a parallelogram with the same base and height. This can be visually seen by splitting a parallelogram into two congruent triangles.
Is the order of the sides important in the formula for the area of a triangle?
No, the order of the sides in the formula for the area of a triangle is not important. As long as the base and height are correctly identified, the result will be the same regardless of the order in which they are multiplied.
Can the formula for the area of a triangle be used for all types of triangles?
Yes, the formula for the area of a triangle (0.5 x base x height) can be used for all types of triangles, including equilateral, isosceles, and scalene triangles. The only requirement is that the base and height must be correctly identified and measured.
How do I calculate the area of a triangle with non-right angles?
To calculate the area of a triangle with non-right angles, you can use the formula 0.5 x base x height x sin(angle), where "angle" refers to the measure of the non-right angle. This formula is derived from the trigonometric formula for the area of a triangle (0.5 x base x height x sin(angle)).