7th Grade Georgia Standard of Excellence: 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 three-dimensional 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.
V = (Area of base) x (Height) Volume GMAS Formula Sheet gives the following formula for the volume of right prisms: V = (Area of base) x (Height) Area of the base is just lw or length x width The height is how tall it is. Huh? What? Pardon Me?
Volume of a Rectangular Prism (Review from 6th grade) What is the shape of the base? rectangle Find area of the base. 3x10 = 30 What is the height? 5 Final Answer? 3x10x5 = 150 units³ 3 5 10
Your Turn 4 x 5 = 20 9 (l x w) x h= (4x5) x 9 = 180in Find area of the base. What is the height? Final Answer? 4 in. 4 x 5 = 20 9 in. 9 (l x w) x h= (4x5) x 9 = 180in
Volume of a Triangular Prism What is the shape of the BIG B base? triangle Find the area of base. (5x10)/2 = 25 What is the height? 4 Final Answer? 4(5x10)/2 = 100 units³ 5 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. Front Back Top Bottom Left Right If 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 2 7
How does your net compare? ☺ It’s ok to be different! ☺ Now find the surface area. 4 2 7
Surface Area of a Rectangular Prism . Surface Area of a Rectangular Prism . 4 2 7 Front = Back = Top = Bottom = Right = Left = Total =
Rectangular Prism Front = 4x7=28 Back = 4x7=28 Top = 2x7=14 Bottom = 2x7=14 Right = 2x4=8 Left = 2x4=8 Total = 100 units ²
Nets Draw a net of a triangular prism. How many faces? 4in. 2 in.
Parts of the Triangular Prism Triangle Rectangle 4in. 2 in. 5 in.
Add the Parts of the Triangular Prism Triangle Rectangle Total = 4in. ½bh= ½(5x4) =10 ½bh= ½(5x4) =10 2 in. lw=5x2 = 10 lw=5x2 = 10 5 in. lw=5x2 = 10 50 in
Pyramid Net 6 ft Draw a net for the square pyramid 5 ft 5 ft
Use the net to name the parts of the pyramid. Square Triangle 5 ft 5 ft
Write Formulas & Compute lw = ½ bh= 5x5 = ½ (5x6)= 25 15 85ft Square Triangle