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Module 9: Geometry

Area

Area is a 2D property measuring the space covered by a shape. This is calculated using the side lengths of a shape and differs depending on the shape. As for 3D shapes, the equivalent property is surface area, the total area covered by each face of the shape. Some examples are included in the tables below.

In these tables, A {"version":"1.1","math":"A"} = area, l {"version":"1.1","math":"l"} = length, w {"version":"1.1","math":"w"} = width, h {"version":"1.1","math":"h"} = height.

2-Dimensional (2D) Areas

Shape Shortcuts and Equations
Triangle A = b h 2 {"version":"1.1","math":"A=\dfrac{bh}{2}"}

Where b {"version":"1.1","math":"b"} = base of triangle (determined by you) and h {"version":"1.1","math":"h"} = height of triangle (vertical distance from base to top point of triangle that is perpendicular to base)
Square A = l 2 {"version":"1.1","math":"A=l^2"}
Rectangle/Parallelogram

(with 2 sets of identical sides)

 A = l w {"version":"1.1","math":"A = lw"}

For a parallelogram A = b h {"version":"1.1","math":"A=bh"}, where h {"version":"1.1","math":"h"} = vertical height and b {"version":"1.1","math":"b"} = base.
Trapezoid A = a + b 2 h {"version":"1.1","math":"A=\dfrac{a+b}{2}h"}

Where a {"version":"1.1","math":"a"} is parallel to the base, b {"version":"1.1","math":"b"}, and h {"version":"1.1","math":"h"} is the vertical height.
Circle The area is determined using the radius.

A = 2 π r {"version":"1.1","math":"A=2\pi r"}

3-Dimensional (3D) Areas

Shape Shortcuts and Equations
Cube S A = 6 l 2 {"version":"1.1","math":"SA=6l^2"}
Rectangular Prism S A = 2 ( l w + l h + h w ) {"version":"1.1","math":"SA=2(lw+lh+hw)"}

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