Pyramids
A pyramid is a 3D shape with flat A plane surface of a geometric solid. A cube has 6 faces; a tetrahedron, 4 faces.. The base of a pyramid is a polygon and is used to describe the pyramid (eg a square-based pyramid, triangle-based pyramid etc). Its sides are triangles which meet at the top.
Volume
The The volume of a three-dimensional shape is a measure of the amount of space or capacity it occupies, eg an average can of fizzy drink has a volume of 330 ml. of a pyramid can be calculated using the formula:
\(\text{volume of a pyramid} = \frac{1}{3} \times \text{area of base} \times \text{perpendicular height}\)
The If the angle between two lines is a right angle, the lines are said to be perpendicular. height (h) is the height of the pyramid measured at a right angle from the base.
Surface area
The surface area of a pyramid can be calculated by adding the area of the base to the sum of the areas of the triangular faces.
Question
Find the area of this square-based pyramid:
The area of the base is \(5 \times 5 = 25~\text{cm}^2\).
The area of each triangular face is \((5 \times 6) \div 2 = 15~\text{cm}^2\).
There are four identical triangular faces, so the total surface area is \(25 + 4 \times 15 = 85~\text{cm}^2\).
More guides on this topic
- NEW: Angles
- NEW: Angles in parallel lines
- NEW: Polygons
- NEW: Line and rotational symmetry
- NEW: Constructing triangles
- NEW: Ruler and compass constructions
- NEW: Loci
- NEW: Bearings
- NEW: Perimeter
- NEW: Area
- NEW: Volume of a prism
- NEW: Surface area of a prism
- NEW: Pyramids, cones and spheres
- NEW: Nets, plans and elevations
- NEW: Circumference and arc length
- NEW: Area of circles and sectors
- NEW: Higher – Calculating angles using circles
- NEW: Higher – Using the alternate segment theorem, tangents and chords
- NEW: Reflection
- NEW: Rotation
- NEW: Translation
- NEW: Enlargement
- NEW: Higher − Negative enlargements
- NEW: Higher – Combined transformations and invariant points
- NEW: Congruent and similar shapes
- NEW: Higher – Similarity in 2D and 3D shapes
- NEW: Pythagoras' theorem
- NEW: Solving 2D and 3D problems using Pythagoras' theorem
- NEW: Right-angled trigonometry
- NEW: Higher – Sine rule – OCR
- Angles, lines and polygons - OCR
- Loci and constructions - OCR
- 2-dimensional shapes - OCR
- Circles, sectors and arcs - OCR
- Circle theorems - Higher - OCR
- Transformations - OCR
- Pythagoras' theorem - OCR
- Units of measure - OCR
- Trigonometry - OCR
- Vectors - OCR
