TEAS® Math Study Guide
Geometric Quantities
Geometric Quantities
To find the area and perimeter of common two-dimensional shapes, use the following formulas:
Square
- Area: \(\text{side} \times \text{side}\)
- Perimeter: \(4 \times \text{side}\)
Rectangle
- Area: \(\text{length} \times \text{width}\)
- Perimeter: \(2 \times (\text{length} + \text{width})\)
Triangle
- Area: \(\dfrac{1}{2} \times \text{base} \times \text{height}\)
- Perimeter: \(\text{sum of all three side lengths}\)
To find the area and perimeter of irregular (complex) polygons:
- Area: divide the shape into squares, rectangles, or triangles. Find the individual areas of each shape and then add them all together.
- Perimeter: Add all outer sides together.
To find the volume of common three-dimensional shapes, use the following formulas:
| Shape | Volume Formula | Notes |
| Cube | \(V = s^3\) | \(s = \text{length of the side}\) |
| Rectangular Prism | \(V= l \times w \times h\) | \(l = \text{length}, \ w = \text{width}, \ h = \text{height}\) |
| Cylinder | \(V = \pi \times r^2 \times h\) | \(r = \text{radius}, \ h = \text{height}\) |
|
Cone |
\(V = \dfrac{1}{3} \times \times \pi \times r^2 \times h\) | \(r = \text{radius}, \ h = \text{height}\) |
Tips:
Always match or convert units before solving.
Use the approximation π = 3.14 unless stated otherwise in the question.
A quick sketch can help visualize the shapes.