When a plane cuts through an object, an area is projected onto the plane. Any plane can be used to cut through the surface, but when that plane is perpendicular to an axis of symmetry, its projection is called a cross-sectional area. For a simple three-dimensional shape, such as a cylinder, the cross-sectional projection is a circle, and the area is easy to calculate. With such shapes as an I-beam, however, calculating the cross-sectional area can be complicated.
Identify the axis of symmetry. For many applications, this will be the longest axis or the longitudinal axis.
Identify the shape projected onto a plane that passes through the shape perpendicular to the axis of symmetry. If the shape is complex, divide it into simpler shapes for ease of calculation. An I-beam, for example, can be divided into a horizontal rectangle on the top, a horizontal rectangle on the bottom and a vertical rectangle connecting them in the middle.
Select the appropriate area formulas to use for the calculation. Some common ones are:
Triangle: A = 0.5bh
Rectangle: A = bh
Circle = (pi)r^2
Measure the values needed to fill in the formula(s).
Solve the area equations. For complex geometries, solve the simpler equations and add them together to get the total cross-sectional area.
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