Rectangular Pyramid 6' x 3' x 5'

Figure Eight: Rectangular Pyramid

Dimensions: Base 6’ x 3’ ; Height of 5’

SCALE MODEL

Net Sketch on Paper (need graphic)

For the Euclidean construction, use your compass and straight edge to construct each of the perpendicular lines. Let 1 foot be represented by half an inch in this model so it will fit on a regular sheet of paper.

Rectangular Base

Draw a 3 inch x 1 1/2 inch square in the middle of your paper. Use the 3x5 card to guide you.

Lateral Faces

    • Locate the midpoint of each side of the square. Use your compass to do this step.
    • Use a 3x5 card to draw a guide line from the midpoints perpendicular to each side.
    • On the 3 inch sides, measure and draw 2 5/8 inch segments on each guideline (where did this measurement come from?)
    • On the 1 1/2 inch sides, measure and draw 2 7/8 inch segments on each guideline (where did this measure come from?)
    • Note that because the base is a rectangle, the dimensions for the adjacent lateral faces of the base are different.
    • Connect to form a triangle on each edge of the square.
    • When you are done, cut out the net and fold as necessary.
    • Do not glue or tape the edges together unless your teacher tells you to.

Create the Net in SketchUp (Scale Model)

Find the Lateral Surface Area and Volume

Step 1a - Find the slant height for the skinny triangles

Step 1b - Find the slant height for the fat triangles

Step 2 - Find the area of the skinny and fat triangular faces

Step 3 - Find the lateral surface area

Find the Volume

Find the lateral edges