ASVAB Geometry Formulas Study Sheet

Geometry Formulas for ASVAB Study Sheet

Rectangles and Squares (Very Common)

• Area (A):

  • Formula: $A = l \times w$
  • Where:
  • $l = \text{length}$
  • $w = \text{width}$

• Perimeter (P):

  • Formula: $P = 2l + 2w$
  • Square shortcut (for all sides equal):
  • Formula: $P = 4s$
    • Where:
    • $s = \text{side length}$

Triangles

• Area (A):
  • Formula: $A = \frac{1}{2}bh$
  • Where:
  • $b = \text{base}$
  • $h = \text{height}$
  • Important: The height must be perpendicular to the base.

Circles (Know These Cold)

• Area (A):

  • Formula: $A = \pi r^2$
  • Where:
  • $r = \text{radius}$

• Circumference (C):

  • Two formulas:
  • $C = 2\pi r$
  • OR:
    • $C = \pi d$
    • Where:
    • $d = \text{diameter} = 2r$

Note: Use $3.14$ for $\pi$ unless told otherwise.

Parallelograms

• Area (A):
  • Formula: $A = b \times h$
  • Important: Use the vertical height, not the slanted side.

Trapezoids (Occasional)

• Area (A):
  • Formula: $A = \frac{(b<em>1 + b</em>2)}{2} \times h$
  • Where:
  • $b<em>1, b</em>2 = \text{parallel sides}$
  • $h = \text{height}$

3D Shapes (Ice-Level Only)

• Rectangular Prism (Box):

  • Volume (V):
  • Formula: $V = l \times w \times h$
    • You may encounter this as:
    • “How much space does it hold?”

• Cylinder (Rare, but possible):

  • Volume (V):
  • Formula: $V = \pi r^2 h$

Angles (Conceptual)

• Straight Line:

  • Sum: $180°$

• Circle:

  • Sum: $360°$

• Right Angle:

  • Measure: $90°$

• Triangle Interior Angles:

  • Sum = $180°$

Pythagorean Theorem (Limited Use)

• Applicable only for right triangles:

  • Formula: $a^2 + b^2 = c^2$
  • Where:
  • $c = \text{hypotenuse (longest side)}$

• Example:

  • For a triangle with sides 3 and 4:
  • Calculation:
    • $3^2 + 4^2 = 9 + 16 = 25$
    • Therefore, $c = 5$