Presentation on theme: "Surface Area Introduction and SA Formula for Rectangular Prisms"— Presentation transcript:
1 Surface Area Introduction and SA Formula for Rectangular Prisms
2 REMEMBER THE PARTS OF SOLIDS? 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.
4 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.
5 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.
6 lwhNotice 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.
7 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 asS = 2ℓw + 2wh + 2ℓh.NOTE: Add this formula onto your notes sheet for PRISMS – under the Volume formula. Head it “Surface Area of a Rectangular Prism”
9 Examine the net of the prism Examine the net of the prism. The base of the rectangle is equal to the perimeter of the base of the prism.
10 BabcP = a + b + cNOTE: Add this formula (S = Ph + 2b) onto your notes sheet for PRISMS – under the Surface Area formula for rectangular prisms. Head it “Surface Area of a Right Prism”
11 The surface area formula is only true for right prisms 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!
12 Example 1Find the surface area of the rectangular prism with the following dimensions:l = 14, w = 2, h = 15P = =32B=14*2=28SA = 15*32+2*28=536 units2
13 Example 2Find the surface area of the rectangular prism with the following dimensions:l = 3’, w = 6’, h = 2.5’P = 3*2+6*2=18B=3*6=18SA = 2.5*18+2*18=81ft2
14 Equilateral base with 6” sides Example 3Find the surface area of the regular triangular prism with the following dimensions:Equilateral base with 6” sidesPrism height 14”Use triangles to find the height of the triangular base.B = 0.5*6*3√3=9√3P = 6+6+6=18SA = 14*18+2*9√3= in2
15 Example 4 Work backwards to solve for the unknown information. In a rectangular prism, SA = 560ft2, and the base is 7 ft by 8 ft. What is the height?560=h*560=30h+112448=30hh=14.93 ft
16 Example 5 Work backwards to solve for the unknown information. In a regular hexagonal prism, the base sides are 18 cm, and theSA = cm2. What is the height of the prism?Use triangles to find the apothem of the hexagon (9√3)=h*108+2*.5*9√3*108=108hH= = 25 cm
17 SA = 197.87 in2. What is the height of the prism? Example 6Work backwards to solve for the unknown information.In a isosceles triangular prism, the base legs are 4 in, and base is 6 in; and theSA = in2. What is the height of the prism?Split the triangular base in half and use the Pythagorean Theorem (or trig) to solve for the height (√7)197.87=h*14+2*3√712.999=h=13in