A cross-sectional area is the area where a two-dimensional plane intersects a three-dimensional object, such as a sphere, cube, cone or cylinder. To calculate this area, first determine the shape of the intersected area, select the appropriate formula based on this shape, measure or calculate the variables needed, and input the data into the formula. Cross-sections are typically parallel or perpendicular to the base of the three-dimensional object.
A parallel cross-section of a sphere, cone or cylinder is a circle. To calculate the area, find the radius of the circle at the cross-section, square it, and multiply by pi, a number most commonly simplified to 3.14. The perpendicular cross-section of a cone is a triangle, and the same cross-section of a cylinder is a square. A parallel or perpendicular cross-section of a cube or rectangular prism is a rectangle. Multiply the length by the width to find the area.
A rectangular pyramid has a parallel cross-section of a rectangle and a perpendicular cross-section of a triangle. The parallel cross-section of a triangular prism or pyramid is a triangle. For a triangle, multiply the base by the height, and divide by two to get the area.
Much less common, a doughnut-shaped object has two cross-sections. The parallel cross-section is two identical circles, and the perpendicular consists of two concentric circles called an annulus.