Hexagonal Pyramid Calculator

Base Edge: 4, Height: 10 Step 1: Base area = (3√3/2) × 16 = 41.569 Step 2: Apothem = (√3/2) × 4 = 3.464 Step 3: Slant height = √(100 + 12) = 10.583 Step 4: Lateral area = 3 × 4 × 10.583 = 126.996 Step 5: Total SA = 168.565 Step 6: Volume = (1/3) × 41.569 × 10 = 138.564

A hexagonal pyramid is a three dimensional geometric shape characterized by a hexagonal base and six triangular faces that meet at a single point called the apex. The "regular" in regular hexagonal pyramid means its base is a regular hexagon, where all six sides and angles are equal, and its apex is directly above the center of the base. This symmetry is crucial for many calculations involving its dimensions. Key components include the base edge length (a), which defines the size of the hexagonal base, and the pyramid height (h), representing the perpendicular distance from the apex to the center of the base. Another important dimension is the slant height, which is the height of each triangular face from the midpoint of its base edge up to the apex. Understanding these elements is fundamental to calculating the pyramid's volume, which measures the space it occupies, and its surface area, which is the total area of all its faces, including the base. Its unique shape offers interesting challenges and applications in design and engineering.