Area Volume Blueprint Worksheet
Area & Volume Blueprint
Master Formula Reference Guide • 2D Area & 3D Volume
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Part 1 • 2D Surface Area Formulas (\(A\))
Measured in Square Units (\(\text{units}^2\))
Square 4 Equal Sides
side (s) s
\(A = s^2\)
\(s\) = length of any side
\(A = \text{side} \times \text{side}\)
Rectangle Base × Height
length (l) w
\(A = l \cdot w\)
\(l\) = length, \(w\) = width
Also written \(A = b \cdot h\)
Triangle Half Rectangle
base (b) h
\(A = \frac{1}{2} b h\)
\(b\) = base, \(h\) = height (\(\perp\))
Also written \(A = \frac{bh}{2}\)
Trapezoid Average Bases
base₁ (b₁) base₂ (b₂) h
\(A = \frac{b_1 + b_2}{2} h\)
\(b_1, b_2\) = parallel bases
\(A = \frac{1}{2}(b_1 + b_2)h\)
Part 2 • 3D Solid Volume Formulas (\(V\))
Measured in Cubic Units (\(\text{units}^3\))
Cube All Equal Edges
side (s) s s
\(V = s^3\)
\(s\) = length of any edge
\(V = s \times s \times s\)
Cube has 6 identical square faces
Rectangular Prism Box Volume
length (L) H W
\(V = L \cdot W \cdot H\)
\(L\) = length, \(W\) = width, \(H\) = height
\(V = \text{Base Area } (B) \times H\)
Also written \(V = l \cdot w \cdot h\)
Triangular Prism Special Formula
width (W) H length (L)
\(V = \frac{LWH}{2}\)
\(V = (LWH) / 2\)
\(L\) = prism length, \(W\) = base, \(H\) = height
Exactly half of a rectangular prism!
The Perpendicular Height Rule (\(\perp\))
In triangles, trapezoids, and triangular prisms, height (\(h\) or \(H\)) is always measured perpendicular to the base at a \(90^\circ\) right angle—never along a slanted side.
Dimensional Units Guide
• 2D Area (\(A\)): 2 dimensions multiplied → \(\text{cm}^2, \text{m}^2, \text{ft}^2, \text{in}^2\)
• 3D Volume (\(V\)): 3 dimensions multiplied → \(\text{cm}^3, \text{m}^3, \text{ft}^3, \text{in}^3\)
Geometry Formula Reference Blueprint • Middle & High School Mathematics Reference Sheet • Formula Guide
