T-Shape Calculator

Calculations at a T-shape. This is a special shape of a concave octagon, made of two perpendicular rectangles. The vertical shaft is placed in the middle of the horizontal beam.
Enter length and thickness of beam and shaft, choose the number of decimal places and click Calculate.

	Beam length (a):
	Beam thickness (b):
	Shaft length (c):
	Shaft thickness (d):
	Arm length (a'):
	Height (h):
	Perimeter (p):
	Area (A):
	Round to   0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15   decimal places.

Lengths, thicknesses, height and perimeter have the same unit (e.g. meter), the area has this unit squared (e.g. square meter).

In this T-shape, the beam and shaft can have different thicknesses. However, in many shapes of this type, the thickness of these two rectangles is the same. The T-shape has eight right angles, six of which are convex and two concave. The convex right angles of course are calculated as 90 degrees, but the two concave right angles are calculated as 270 degrees, so that also here the sum of the angles of an octagon is 1080 degrees, as it should be.
The T-shape has exactly one axis of symmetry, which runs vertically and centrally across the beam widthwise and across the shaft lengthwise. It has no other symmetries.
This type of shape is used, for example, as a cross-section in T-beams, which are often made of steel and must support heavy loads.

Other shapes named after letters are the L-shape, the H-shape, and the X-shape. This could, of course, be done with any letter of the alphabet, but these four seemed to have the most universal geometric shapes; they were the most obvious. The L-shape and H-shape are also composed of rectangles, while the X-shape consists of two intersecting parallelograms. Other possible letter shapes include the elliptical ring as an O-shape and the sharp kink as a V-shape.