General Prisms 1 of 8 Boardworks 2012 Information

General Prisms 1 of 8 © Boardworks 2012

Information 2 of 8 © Boardworks 2012

Prisms A prism is a polyhedron with two congruent faces, called bases, that lie in parallel planes. The other faces, called lateral faces, are rectangles formed by connecting the corresponding vertices of the bases. This is called a hexagonal prism because its cross-section is a hexagon. A prism has the same cross-section throughout its length. 3 of 8 © Boardworks 2012

Surface area of a prism Below is the net of a triangular prism. What is its surface area? 13 cm 260 60 200 12 cm 260 10 cm 20 cm 4 of 8 60 Find the area of each face, then write it in the diagram of the net. area of triangles: 1 triangles = 2 × 10 × 12 triangles = 60 area of rectangles: sides = 13 × 20 sides = 260 base = 10 × 20 base = 200 add surface area of each face: 60 + 200 + 260 840 cm 2 © Boardworks 2012

Finding surface area from a net 5 of 8 © Boardworks 2012

Volume of a prism The volume of a prism is found by multiplying the area of its cross-section A by the length l of its lateral face (or by its height if it is standing on its cross-section). l h A V = Al 6 of 8 A V = Ah © Boardworks 2012

Volume of a prism What are the volumes of these prisms? Area of cross-section = 0. 5 × 4 = 10 cm 2 Volume of prism = 10 × 7. 2 = 72 cm 3 Area of cross-section = (7 × 12) – (4 × 3) = 84 – 12 = 72 m 2 Volume = 72 × 5 = 360 m 3 7 m 7. 2 cm 3 m 12 m 4 m 4 cm 5 cm 7 of 8 5 m © Boardworks 2012