Pyramid Solutions

Figure Six – Square Pyramid I

Dimensions Base 6’ x 6’; Height of 5’

Graphics are used to illustrate the missing dimensions. I use a "cutaway" model to show the

"inside" of the pyramid. When finding surface area, I stress visualization of the shape instead of

the use of formulas.

Figure 6 - Cutaway with slant height

1. Use the PT to get the sl_ht SQRT(3^2+5^2) = 5.83 feet

2. Area of one triangular face is 0.5(6*5.83) = 17.49 ft²

3. LSA = 4 * 17.49 = 69.96 ft²

Volume = 1/3(Area of Base * Height) = 1/3(6*6*5) = 60 ft³

Figure Seven - Square Pyramid II

Base 6’ x 6’ ; Slant Height of 5’

Note that the lateral faces are identical triangles with a base of 6' and a triangle height of 5'.

Figure 7a - Net

When the faces are folded up, a 3-4-5 right triangle can be seen inside the pyramid.

Figure 7b - Cut away

1. sl_ht = 5'

2. Area of one triangular face is 0.5(6*5) = 15 ft²

3. LSA = 4*15 = 60 ft²

Volume = 1/3(6*6*4) = 48 ft³

Figure Eight – Rectangular Pyramid

Dimensions 6’ x 3’; Height of 5’

It is important to use the cutaway sketch when finding the slant heights for this pyramid.

Figure 8a. Pyramid

Figure 8b. Pyramid cut away

Figure 8c - Blue Face Area

1a. sl_ht = 5.83 feet

1b. Area = 0.5(3*5.83) = 8.745 ft²

SketchUp confirms the area calculation.

Figure 8d - Yellow Face Area

2a. sl_ht = 5.22 feet

2b. Area = 0.5(6*5.22) =15.66 ft²

SketchUp confirms the area calculation.

3. LSA = 2*8.745 + 2*15.66 = 48.81 ft²

Volume = 1/3(Area of Base * Height) = 1/3(3*6*5) = 30 ft³