Solve for the hypotenuse of a right triangle:

Compute the area of a specific triangle:

Create a geometric scene:

Find the area of the quadrilateral :

Visualize an instance of the scene:

Consider a triangle where two of the three vertices are fixed:

Compute the area of the triangle for any position of the third vertex :

Compute the area of the particular triangle pictured above:

Construct an isosceles triangle with the segments from the vertices to the opposite sides forming the inner angles:

Solve for the measure of the inner angle :

Visualize an instance of the scene:

Construct a scene with two triangles embedded inside a third triangle:

Solve for a ratio of areas of the two inner triangles:

Consider a shaded region defined by a square and a circle:

Compute the fraction of the square covered by the shaded region:

Construct a geometric scene:

Find the area of the triangle and the measure, in radians, of the angle :

Visualize the triangle:

Find an instance of a scene:

Solve for the point a, the distance between points a and c and the area of the triangle in this scene instance:

Solving with a different instance will give different results:

If expr in GeometricSolveValues[scene,expr] is not a list, the result is a list of possible values:

If expr is a list, even a list of one element, the result is a list of lists of possible values:

Results using coordinates of points are represented with Indexed:

Results for abstract scenes, even if they uniquely describe the geometry, are based solely on the description:

Results for concrete scenes are expressed in terms of the coordinates of the scene:

Consider a scene featuring a right triangle with its leg lengths specified but its hypotenuse unknown:

The subvalue "AlgebraicFormulation" of a GeometricScene object gives a conjunction of constraints for that scene to be valid:

The hypotenuse can be solved for using SolveValues on the algebraic formulation or using GeometricSolveValues directly on the scene:

For a generic triangle, there are two possible solutions for the area, only one of which will have the correct sign for a specific numeric instantiation of the parameters: