Surface Area of Prisms.

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Presentation transcript:

Surface Area of Prisms

Vocabulary Surface Area: the sum of the areas of all the faces of a 3D figure Measured in square units (ex: ft2, in2, m2, etc) Faces: sides of a figure Prism: 3D shape with two congruent (equal) bases and parallelogram sides Note: the figure does not have to be sitting on its base

Examples of Prisms Hexagonal Cube Rectangular Prism Triangular Prism Prism

Cube – special because all six faces are identical Find the area of one of the faces Area of square = s2 or bh 3*3 = 9 yd2 Since all six faces are exactly the same, multiply the area of one face by 6 9 yd2 * 6 Surface area = 54 yd2 3 yd 3 yd 3 yd

Practice Cube

Hexagonal Prism – 2 hexagon bases and 6 identical rectangular sides Find the area of one of the hexagons Area of hexagon = 3bh = 3*14*13 = 546 cm2 Find the area of one of the rectangles Area of rectangle = bh = 13*7 = 91cm2 There are 2 hexagons so multiply that area by 2. There are 6 rectangles so multiply that area by 6. Hexagons: 2 * 546 = 1092 cm2 Rectangles: 6 * 91 = 546 cm2 Add the areas together: 1092 + 546 = 1638 cm2 7 cm 14 cm 13 cm

Practice Hexagonal Prism

Triangular Prism – 2 triangle bases and 3 rectangular sides* If base is equilateral triangle, then all three rectangles will be the congruent If base is isosceles or scalene triangle, then rectangles will be different sizes

Equilateral Triangular Prism – all rectangles congruent Find the area of one triangular base Find the area of one rectangular side There are 2 triangular bases so multiply that area by 2. There are 3 rectangular sides so multiply that area by 3. Add the areas together to get the surface area

Scalene Triangular Prism Find area of triangular base Area of triangle = ½ bh = ½ *8*9 = 36cm2 Find area of pink rectangle (bottom side) = bh = 8*5 = 40cm2 Find area of purple rectangle (left side) = bh = 9*5 = 45cm2 Find area of green rectangle (top side) = bh = 10 * 5 = 50cm2 There are two triangular bases so multiply that area by 2 36cm2*2 = 72cm2 Add all four areas together to get total surface area 72cm2 + 40cm2 + 45cm2 + 50cm2 = 207cm2

Practice Triangular Prisms

Rectangular Prism – all sides rectangles 3 pairs of congruent faces Top/bottom Front/back Sides (left/right) General Formula for Surface Area 2lw + 2wh + 2lh = SA Those are “L”s not “1”s ONLY APPLIES TO RECTANGULAR PRISMS

Rectangular Prism Example L = 14cm H = 8 cm W = 7 cm Formula: 2lw + 2wh + 2lh (2*14*7) + (2*7*8) + (2*14*8) 196 + 112 + 224 532 cm2 7 cm 8 cm 14 cm

Rectangular Prism Practice