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Solid Figures 7th Grade Georgia Standard of Excellence: MGSE7.G.6 Solve real-world and mathematical problems involving area, volume and surface area of two- and threedimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms. Gail Sherman 2013 What is a Right Prism? A right prism is a geometric solid that has a polygon as its base and vertical sides perpendicular to the base. The base and top surface are the same shape and size. It is called a “right” prism because the angles between the base and sides are right angles. Volume GMAS Formula Sheet gives the following formula for the volume of right prisms: Pardon Me? V = (Area of base) x (Height) Area of the base is just lw or length x width The height is how tall it is. Volume of a Rectangular Prism (Review from 6th grade) What is the shape of the base? rectangle 3 Find area of the base. 3x10 = 30 What is the height? 5 Final Answer? 3x10x5 = 150 units³ 5 10 Your Turn 5 in. Find area of the base. What is the height? 9 Final Answer? (l x w) x h= (4x5) x 9 = 180in 9 in. 4 x 5 = 20 Volume of a Triangular Prism What is the shape of the BIG B base? 5 triangle Find the area of base. (5x10)/2 = 25 What is the height? 4 Final Answer? 4(5x10)/2 = 100 units³ 4 10 Nets Draw a net of a cube. How many faces? 6 Surface Area of a Cube Let’s name the faces of our cube. If Front Back Top Bottom Left Right each side is 3 inches long, find the surface area. Add the areas of the 6 faces! Front is…… 3x3=9 Back is……. 3x3=9 Top is……… 3x3=9 Bottom is… 3x3=9 Left is……… 3x3=9 Right is……. 3x3=9 And the TOTAL is 54 in² Rectangular Prism Just a box. Draw a net for this rectangular prism. 2 4 7 How does your net compare? 2 4 7 ☺ It’s ok to be different! ☺ Now find the surface area. . Surface Area of a Rectangular Prism . Front = Back = Top = Bottom = Right = Left = Total = 2 4 7 Rectangular Prism Front = 4x7=28 Back = 4x7=28 Top = 2x7=14 Bottom = 2x7=14 Right = 2x4=8 Left = 2x4=8 Total = 100 units ² 2 4 7 Nets Draw a net of a triangular prism. How many faces? 4in. Parts of the Triangular Prism Triangle Triangle Rectangle Rectangle Rectangle 4in. Add the Parts of the Triangular Prism Triangle Triangle ½bh= ½(5x4) =10 Rectangle lw=5x2 = 10 Rectangle lw=5x2 = 10 Rectangle lw=5x2 = 10 Total = 50 in ½bh= ½(5x4) =10 4in. Pyramid Net 6 ft Draw a net for the square pyramid 5 ft Use the net to name the parts of the pyramid. 6 ft Square Triangle Triangle Triangle Triangle 5 ft Write Formulas & Compute Square Triangle Triangle Triangle Triangle lw = ½ bh= ½ bh= ½ bh= ½ bh= 5x5 = ½ (5x6)= ½ (5x6)= ½ (5x6)= ½ (5x6)= 25 15 15 15 15 85ft

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