Presentation on theme: "Surface Area Introduction and SA Formula for Rectangular Prisms."— Presentation transcript:
Surface Area Introduction and SA Formula for Rectangular Prisms
Prisms and cylinders have 2 congruent parallel bases. A lateral face is not a base. The edges of the base are called base edges. A lateral edge is not an edge of a base. The lateral faces of a right prism are all rectangles. An oblique prism has at least one nonrectangular lateral face. REMEMBER THE PARTS OF SOLIDS?
An altitude of a prism or cylinder is a perpendicular segment joining the planes of the bases. The height of a three-dimensional figure is the length of an altitude.
Surface area is the total area of all faces and curved surfaces of a three- dimensional figure. The lateral area of a prism is the sum of the areas of the lateral faces.
l w h Notice from the net there are two of each rectangle. The area of 2 of them will be lw, 2 will be wh, and 2 will be lh.
Surface Area of a Rectangular Prism The surface area of a right rectangular prism with length ℓ, width w, and height h can be written as S = 2ℓw + 2wh + 2ℓh.
Surface Area of Right Prisms
Examine the net of the prism. The base of the rectangle is equal to the perimeter of the base of the prism.
B B a b c P = a + b + c
The surface area formula is only true for right prisms. To find the surface area of an oblique prism, add the areas of the faces. Caution!
Example 1 Find the surface area of the rectangular prism with the following dimensions: l = 14, w = 2, h = 15
Example 2 Find the surface area of the rectangular prism with the following dimensions: l = 3’, w = 6’, h = 2.5’
Example 3 Find the surface area of the regular triangular prism with the following dimensions: Equilateral base with 6” sides Prism height 14”
Example 4 Work backwards to solve for the unknown information. In a rectangular prism, SA = 560ft 2, and the base is 7 ft by 8 ft. What is the height?
Example 5 Work backwards to solve for the unknown information. In a regular hexagonal prism, the base sides are 18 cm, and the SA = cm 2. What is the height of the prism?
Example 6 Work backwards to solve for the unknown information. In a isosceles triangular prism, the base legs are 4 in, and base is 6 in; and the SA = in 2. What is the height of the prism?