A Wedge is a polyhedral solid defined by two triangular faces and three trapezoidal faces. It looks like a doorstop, a tent, or a slice of cheese. In geometry, it is technically known as a general prismatoid.
This shape is unique because the top edge ($c$) can be a different length than the base edge ($a$). If $c=0$, it becomes a sharp pyramid-like wedge. If $c=a$, it becomes a standard triangular prism.
Calculator Features
1. Universal Wedge Support
Most online calculators only handle the “Right Wedge” (where $c=a$). Our tool handles the general case where the top edge tapers, allowing you to calculate volumes for complex shapes like truncated roofs or machine parts.
2. Instant 4-Way Analysis
With just four dimensions, we calculate:
Volume: The internal capacity.
Total Surface Area: For painting or coating.
Slant Height: The length of the sloping side.
Base Area: The footprint.
3. 3D Wireframe View
An isometric wireframe updates in real-time as you type, helping you visualize whether your “Top Edge” is shorter or longer than the base.
Volume & Area Formulas
Let $a$ and $b$ be the base length and width. Let $c$ be the top edge length, and $h$ be the vertical height.
Volume
Volume $V = \frac{h b}{6} (2a + c)$
Surface Area
The total area is the sum of 5 faces: 1 Rectangle Base ($ab$), 2 Triangles ($bh/2 \times 2$), and 2 Trapezoids.
Assuming a symmetric wedge, the slant height $s = \sqrt{h^2 + (b/2)^2}$.
Area $A = ab + bh + s(a + c)$
Common Uses
Construction (Roofs)
A “Gable Roof” is geometrically a triangular prism (wedge with $a=c$). A “Hipped Roof” end is often a tapered wedge. Builders use these formulas to order shingles and insulation.
Mechanical Engineering
Wedges are simple machines. Calculating the volume and mass of a metal wedge is essential for determining the force required to lift loads or split materials.
Packaging
Toblerone chocolate boxes are the most famous example of wedge-shaped packaging (triangular prisms). Designers calculate the surface area to optimize cardboard usage.
Tips for Input
The “Top Edge” (c)
This is the tricky variable. If you are building a standard tent or prism, set $c = a$. If you are making a sharp doorstop that comes to a point, set $c = 0$.
Height Measurement
Measure the vertical height ($h$) perpendicular to the base, NOT the slant height ($s$) along the slope.
Frequently Asked Questions (FAQs)
1. What is a Right Wedge?
A Right Wedge is basically a Triangular Prism lying on its side. In this case, the top edge length equals the base length ($c = a$), and the ends are vertical triangles.
2. Can I calculate the weight?
Yes. Once you have the Volume ($V$), multiply it by the material’s density ($Density \times V$) to find the weight.
3. Is a wedge a pyramid?
Not exactly. A pyramid has a single apex point. A wedge has a top *line* (edge). However, if you set the top edge $c = 0$, the wedge technically collapses into a square-based pyramid.
Final Words
The Wedge Area & Volume Calculator handles the heavy lifting of solid geometry formulas. Whether you are splitting logs, designing roofs, or just doing math homework, this tool ensures your dimensions measure up perfectly.
