Combined Square Prism & Pyramid

Interactive geometry — Volume & Surface Area of a Combined Solid (Pyramid on Square Prism)

← Back to Home

Base Width: 3.0

Prism Height: 3.0

Pyramid Height: 2.0

Measurements

Total Volume:33.00 units³

Prism Volume:27.00 units³

Pyramid Volume:6.00 units³

Total Surface Area:66.00 units²

Slant Height:2.50 units

Formulas

Prism Volume (V_p) = w²h_p

Pyramid Volume (V_k) = ⅓w²h_k

Total Volume (V) = V_p + V_k

Prism LSA = 4wh_p

Pyramid LSA = 2ws (s = slant height)

Total Surface Area = w² + 4wh_p + 2ws

Slant Height (s) = √((w/2)² + h_k²)

How to Use

• Drag to rotate the combined solid in 3D

• Scroll to zoom in / out

• Adjust sliders to change dimensions

• Watch measurements update in real-time

Key Terms

Combined Solid — a 3D shape made by joining two or more basic solids

Square Prism — the lower part with two parallel square faces

Square Pyramid — the upper part tapering to an apex

Slant Height (s) — distance from apex to the midpoint of a base edge of the pyramid

Did You Know?

Combined solids appear everywhere in real life — a house with a pyramid roof, an Egyptian obelisk, a tower with a spire, and a gift box with a pyramidal lid are all combined solids!