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sidebar_label: Area of triangle
---
-[Open a pull request](https://github.com/AllAlgorithms/algorithms/tree/master/docs/area-of-triangle.md) to add the content for this algorithm.
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+A *triangle* is a polygon with three sides and three vertices.
+Calculating its area efficiently depends on what is known about it.
+
+## From base and height
+
+The basic formula assumes knowledge of the length of one of the sides
+(called *base*) and the length of the *height* of the triangle with
+respect to that side. This *height* is the segment that originates from
+the vertex that is *not* on the side we know about, and intersects the
+side we know about at a right angle.
+
+Assuming the base is put horizontally and the third vertex above it, the
+following picture results. Quantity *b* is the length of the bottom
+side, and *h* the height with respect to it.
+
+
+
+Height can sometimes be referred to as *altitude*.
+
+### Formula
+
+In this case, the area is calculated as follows:
+
+
+
+
+### Algorithm
+
+The algorithm can be derived directly from the defining formula above:
+
+```
+triangle_area_basic (b, h) {
+ return b * h / 2;
+}
+```
+
+## In the euclidean plane
+
+In this section, it is assumed that the triangle is known by the
+coordinates of its three vertices A, B, and C on the plane:
+
+
+
+### Formula
+
+In this case, the area of the triangle can be calculated as follows:
+
+
+
+### Algorithm
+
+The following algorithm is a direct translation of the formula:
+
+```
+triangle_area_plane (x_A, y_A, x_B, y_B, x_C, y_C) {
+ return abs((x_B - x_A) * (y_C - y_A) - (x_C - x_A) * (y_B - y_A)) / 2;
+}
+```
+
+## In the euclidean space
+
+In this section, it is assumed that the triangle is known by the
+coordinates of its three vertices A, B, and C in the three-dimensional
+space:
+
+
+
+### Formula
+
+The formula to calculate the area involves calculating the determinant
+of three matrices:
+
+
+
+The absolute value of each determinant is the double of the area of the
+triangle obtained by projecting the target triangle onto one of the
+coordinate planes, which allows reusing the formula for the triangle in
+the plane in a previous section.
+
+### Algorithm
+
+The following algorithm leverages the triangle area calculation in the
+plane, described in a previous section and not repeated here:
+
+```
+/* Assume that A, B, and C are 3-dimensional arrays
+ X at index 0, Y at index 1, Z at index 2 */
+triangle_area_space (A, B, C) {
+ x = triangle_area_plane(A[1], A[2], B[1], B[2], C[1], C[2]);
+ y = triangle_area_plane(A[2], A[0], B[2], B[0], C[2], C[0]);
+ z = triangle_area_plane(A[0], A[1], B[0], B[1], C[0], C[1]);
+ return sqrt(x * x + y * y + z * z);
+}
+```
+
+*Note*: the division by two in the formula is already included in the
+result from the calculation of the area in the plane.
+
+## Performance
+
+All algorithms for calculating the area of a triangle in the sections
+above execute in constant time (O(0)).
+
+## Implementations
+
+| | Language | Link |
+|:-: | :-: | :-: |
+| | | |
+
+## Helpful Links
+
+- [Triangle][]
+- [Area of Triangles and Polygons][]
+
+[Triangle]: https://en.wikipedia.org/wiki/Triangle
+[Area of Triangles and Polygons]: http://geomalgorithms.com/a01-_area.html