Solid Figures 7 th 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

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. What is a Right Prism?

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 6 th 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

Your Turn  Find area of the base.  What is the height?  Final Answer? 4 in. 5 in. 9 in. 4 x 5 = 20 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

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

How does your net compare? ☺ It’s ok to be different! ☺ Now find the surface area

.. Surface Area of a Rectangular Prism  Front =  Back =  Top =  Bottom =  Right =  Left =  Total = 4 2 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 4 2 7

Nets  Draw a net of a triangular prism.  How many faces? 4in. 5 in. 2 in.

Parts of the Triangular Prism Triangle Rectangle 4in. 5 in. 2 in.

Add the Parts of the Triangular Prism Triangle Rectangle Total = 4in. 5 in. 2 in. ½bh= ½(5x4) =10 lw=5x2 = in

Pyramid Net  Draw a net for the square pyramid 5 ft 6 ft

Use the net to name the parts of the pyramid.  Square  Triangle 5 ft 6 ft

Write Formulas & Compute  Square  Triangle lw = ½ bh= 5x5 = ½ (5x6)= ft