Ch 11-4 Surface Area of A Prism C. N. Colón St. Barnabas HS Geometry.

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Presentation transcript:

Ch 11-4 Surface Area of A Prism C. N. Colón St. Barnabas HS Geometry

Objectives Find the surface area of a prism.

Key terms to know In a plane, a polygon is a closed figure that is a union of line segments. A polyhedron is a three dimensional figure that is formed by the union of plane polygon surfaces. The intersection of the faces are called edges. The intersection of the edges are called vertices of the polyhedron.

What is a PRISM? A prism is a polyhedron with two congruent faces, called bases of the prism. The bases lie in parallel planes. The other faces, called lateral faces, are parallelograms formed by connecting the corresponding vertices of each base. Segments that connect the vertices are called lateral edges.

PRISMS The altitude or height of a prism is the perpendicular distance between its bases. In a right prism, each lateral edge is perpendicular to both bases. Prisms that have lateral edges that are not perpendicular to the bases are oblique prisms. The length of the oblique lateral edges is the slant height of the prism.

PRISMS Prisms are classified by the shape of their bases. For example, the previous figures showed one right rectangular prism and one triangular prism. The surface area of a polyhedron is the sum of the areas of all of its faces. The lateral area of a polyhedron is the sum of the areas of its lateral faces.

Ex. 1: Find the surface area of a prism Find the surface area of a right rectangular prism with a height of 8 inches, a length of 3 inches, and a width of 5 inches.

The Parallelepiped A parallelepiped is a prism that has parallelograms as bases. (See page 442) A rectangular parallelepiped is a parallelepiped that has rectangular bases and lateral edges that are perpendicular to the bases. It is another name for a rectangular pyramid.

Ex. 2: Triangular Prism NOTE: The formula for the area of an equilateral triangle:

Nets Imagine that you cut some edges of a right hexagonal prism and unfolded it. The two- dimensional representation of all of the faces is called a NET.

Nets In the net of the prism, notice that the lateral area (the sum of the areas of the lateral faces) is equal to the perimeter of the base multiplied by the height.

HOMEWORK p. 444 # 3 – 18 (even)