Calculate Area Under an Angle
Calculator for the area from the angle and the length of the legs. An angle with two legs of equal length that are connected at the end results in an isosceles triangle. Please enter the angle in degrees and the length of the legs to calculate the other values.
c is the distance between the two ends of the legs, l is the length of the angle bisector between the angle and c. The isosceles triangle, whose area is calculated here, is spanned between the two legs a and c.
Example: with an angle of 55° and a length of the legs of 5.6 cm, the distance (the base of the isosceles triangle) is 5.2 cm, the length of the bisector is 5 cm and the area is 12.8 cm².
Here you can convert radian into degrees.
At a 90-degree angle, the triangular area formed by this angle is a right isosceles triangle, or in other words, a diagonally bisected square. This is particularly easy to calculate, since the area of the square is a², or a*a, and the area of the bisected square is then a²/2. If the angle is acute, meaning less than 90 degrees, then the corresponding area is smaller than that of the right triangle. For an obtuse angle, i.e., one between 90 and 180 degrees, the area of the triangle is also smaller, even though the length of the distance c continues to increase. However, the length of the angle bisector l to the point of intersection with c becomes shorter again, and this decrease is more pronounced than the increase of the length c. The reason for this is that the tangent increases faster than the cosine. For angles of 180 degrees and above, this area is not defined, and the calculator will not provide a result.