This is the most difficult way to enter the points, because now we have to measure the distance between two adjacent points, and the angle that is created between three adjacent points (the 2^{nd} point is the vertex of the angle). But, it is also the most accurate method, and it is the only method that we can use when we want to calculate the surface of a small area or solve a geometrical problem!

As with the other two methods, the first thing that we need to do is to enable it in the Settings screen. This is relative easy, as it requires to disable both the GPS device and Entering the Longitude/Latitude of the points.

Next we go to the “Points” screen to start adding the points. Here, we notice two buttons in the top right corner: The “compass” button and the “+” button.

## Create a regular polygon

iTopography is equipped with a nice tool to automatically create a regular polygon with as many vertices as we like. For that, we click on the “compass” button, and we then enter the number of vertices and the length of each side.

We decided to create a regular decagon. When we click on the “Done” button, iTopography added the points that we need to create that polygon.

### Analyzing the points

As we see in the list of points for a regular decagon, the first point is a dummy point. This means that it does not matter which point we mark as point 1 of the area that we are interested in. The second point is located on the left of the first and last point, and the distance between that point and the 1^{st} point is 1m. This means that if we were inside the decagon, and we were walking from the last point towards the first point, we would meet the second point on the left hand side. Thus, when we would arrive at the 1^{st} we would turn left for 144^{o} and walk for 1m until we meet the 2^{nd} point. We repeat this process for the other points. Not, hard, right?

## Enter distance/length and angle for each point

Unfortunately, most shapes are not regular polygons, and thus we need to manually enter the distance/length between the points and the angles. This can be cumbersome as we now need to measure each distance/length and each angle separately, but, iTopography has a complex algorithm that allows us to skip few angles.

### Skip few angles

We demo this case by solving the 3^{rd }problem from the site https://www.analyzemath.com/high_school_math/grade_10/geometry.html which has geometrical problems for the 10^{th} grade. In the next screenshot we depict the shape whose area we want to calculate. Note, that we have numbered the 4 corners.

Next, we start the iTopography app, and in the “Points” screen we select iTopography to compute the angles. For the 1^{st} we entered the length to be 15m, and the angle to be 90^{o} (right angle). For the other three points, we only give their distance/length. We end up with the following list of points:

Don’t worry that it says that each point is on the left side of the previous points. Because, they are on the left side, the drawing that we see in the “Map” screen is a mirror image of the drawing that we were asked to compute its surface. Still, in the “Map” screen, at the top right corner we see that the surface of that area is 144m^{2} and the perimeter is 54m.

We end this example, with one more nice feature. We go to the “Calculate” screen, and we click on the notepad button, the one in the top right corner. In the new screen we see the distance between each point and the angle of each vertex.

We already know that the angle of vertex 4 is 90^{o} (we entered this value for point 1), but we also note that the angle of vertex 2 is 90^{o}.

### Enter all angles

Now, we will try to compute the surface of the following area. In this problem, all angles and all distances are known. Note, that each corner is numbered.

We click on the “+” button, and we select that we will enter all angles. As with the regular polygon, the first point is a dummy point. We click again on the “+” to enter the 2^{nd} point. This point, is located on the right of point 1, the distance is 1m, and the angle is 120^{o}. Similarly, the 3^{rd} is on the right of the 2^{nd} point, 0.5 m away, and the angle is 60^{o}. The 4^{th} point is a little bit tricky, as it is located on the left of the 3^{rd} point. We keep repeating this process until we add all 6 points. In the next screenshots we see the list of points, the drawing, and the computed angle for all vertices.

In the last screenshot we note that the angles for a few vertices are not equal to the ones we provided in the 1^{st} screenshot. On the other hand, the distances are the same. This is because we made a small mistake when we measured the distance between the points. The correct distance between point 5 and 6 is 1.866m, and not 1.86, If we modify the length for point 6, and set it to 1.866m, the angles are the one we provided, as we see in the next two screenshots.

Even though in the list of points we see the value of 1.87m, if we tap on that row, in the dialog we see the correct value, i.e. 1.866m. This is because iTopography is rounding the values to two decimals. Note, that when we had given the “wrong” value of 1.86m, iTopography was still able to draw the area, and compute its surface by modifying the angle of a few points. This is the power of the iTopography application!

## Summary

In this article we described how to manually enter the distance/length between points and the angle at each vertex. This is certainly cumbersome as it requires to measure each distance and each angle. But, iTopography is an extremely powerful application, and it has some really nice features:

- If we make a small mistake in the measurement of a distance or an angle, iTopography will still be able to draw the area, and compute its surface/perimeter
- There is a tool for creating regular polygons of any number of vertices
- We may not provide all angles, as, iTopography has a sophisticated algorithm to solve such problems.