Area of Triangle: Find the Unknown Formula

In summary: Area is the amount of space enclosed by a figure.In summary, the student is looking for a way to find the area of a triangle without knowing the formula. A basic calculus equation can be used, but the student is not looking for an extremely advanced one. After some vector and geometric manipulation, the student is able to find the area of a triangle.

Homework Statement

Find the area of a triangle, assume that you don't know the formula of area of any other figure.

The Attempt at a Solution

Well, i was trying to figure out how to find the area of a triangle out of nowhere, but could not get it. I want to know how it was formulated for the very first time. Please help me out (remember that you cannot use any other area formula) . You can use basic calculus, but not very advanced one.

Can you cut the triangle and arrange the pieces so they make a rectangle?

Please show me how to do it.

Please show me how to do it.
PF rules require YOU to make an attempt first, before asking for help.

Homework Statement

Find the area of a triangle, assume that you don't know the formula of area of any other figure.
Not even the area of a rectangle?

Try using box method of area

Homework Statement

Find the area of a triangle, assume that you don't know the formula of area of any other figure.

The Attempt at a Solution

Well, i was trying to figure out how to find the area of a triangle out of nowhere, but could not get it. I want to know how it was formulated for the very first time. Please help me out (remember that you cannot use any other area formula) . You can use basic calculus, but not very advanced one.
Wrong requirement. USE knowledge of area of a rectangle! This will let you form a diagram like a construction to develop formula for area of a triangle.

You don't need to know anything else, just VECTOR and GEOMETRIC manipulation will suffice.

Capitalised are hints.

Thanks.

Find the area of a triangle, assume that you don't know the formula of area of any other figure.
Well, you can know the fromula of a triangle since it isn't any other figure.

1. What is the formula for finding the area of a triangle?

The formula for finding the area of a triangle is A = 1/2 * base * height, where A represents the area, the base is the length of the triangle's base, and the height is the perpendicular distance from the base to the opposite vertex.

2. How do you find the base and height of a triangle?

The base and height of a triangle can be found by measuring the length of the base and the perpendicular distance from the base to the opposite vertex. Alternatively, if the coordinates of the three vertices are known, the base and height can be calculated using the distance formula.

3. Can the formula for finding the area of a triangle be used for all types of triangles?

Yes, the formula A = 1/2 * base * height can be used for all types of triangles, including equilateral, isosceles, and scalene triangles. However, the base and height may need to be calculated differently depending on the type of triangle.

4. How do you determine the units for the area of a triangle?

The units for the area of a triangle will depend on the units used for the base and height. If the base and height are measured in inches, the area will be in square inches. If they are measured in meters, the area will be in square meters. It is important to use consistent units for accurate calculations.

5. Can the formula for finding the area of a triangle be used for other shapes?

No, the formula A = 1/2 * base * height is specific to triangles and cannot be used for other shapes. Other shapes, such as squares, rectangles, and circles, have their own unique formulas for finding the area.