# Find Area of Triangle Using No Formula

• ns5032
In summary, there are several ways to find the area of a triangle with sides a, b, and c without using a formula like Heron's Formula. One method is to split the triangle into two right angle triangles and calculate the area of each one separately. Another method is to define a line as a side of the triangle and use integration, although this may be more complex and require breaking the triangle into right triangles first. Ultimately, it may be simpler to follow mgb_phys' recommendation and directly calculate the area of the right triangles.
ns5032
How can I go about finding the area of a triangle with sides a, b, and c, assuming we do not already know a formula for it (such as Heron's Formula)? Kind of like a proof, I suppose.

You could split it into 2 right angle triangles. It's failry easy to calculate the area of a right angle triangle.

define a line as a side and integrate...

PowerIso said:
define a line as a side and integrate...
I take it you mean set the triangle up so that one vertex is at the origin and another is along the positive x-axis. The difficulty with that is that, since you know only the lengths of the sides, you would have to break it into right triangles to determine the limits of integration. Once you have done that, it is simpler to find the area of the right triangles, mgb_phys' recomendation, than to integrate.

## 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 one side of the triangle, and the height is the perpendicular distance from the base to the opposite vertex.

## 2. Can the area of a triangle be found without using a formula?

Yes, the area of a triangle can be found using other methods such as finding the area of a rectangle and then dividing it in half, or by using trigonometric functions.

## 3. How do you find the area of a triangle using no formula?

One way to find the area of a triangle without using a formula is by breaking it into smaller shapes, such as rectangles or trapezoids, and then finding their areas and adding them together.

## 4. Can you find the area of any type of triangle without using a formula?

Yes, the area of any type of triangle can be found without using a formula by using basic geometric principles, such as dividing the triangle into smaller shapes or using trigonometric functions.

## 5. Why would someone want to find the area of a triangle without using a formula?

There are several reasons why someone might want to find the area of a triangle without using a formula. For example, it can be a good exercise in geometry and problem-solving skills, or in situations where a formula is not readily available, such as in real-life scenarios or when working with non-standard triangles.

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