 Source: Pyramid Arena, Exothermic, Flickr

Recall from the lesson introduction that the Pyramid Arena is a regular rectangular pyramid in Memphis, Tennessee.

Suppose that Marshall has been contracted to resurface the exterior of the Pyramid Arena using solar electricity panels. Before he can start, he needs to know exactly how much material it will take for him to resurface this regular pyramid.

Before beginning, let’s examine the problem situation more closely.

Marshall is provided the height of the Pyramid Arena, 321 feet, and the length of each base edge of the pyramid, 590 feet, as shown in the diagram below. In most problem situations, the slant height of a pyramid will be given. However, sometimes, as in the situation with Marshall and the Pyramid Arena, you will have to find the slant height using the information given in the problem. Watch the video below to see how the slant height can be calculated when you know the height of the pyramid and the base edge length.

The images below summarize how the slant height was calculated in the video.

Using the side view of the pyramid, you see that the height of the pyramid is perpendicular with the base. Therefore, a right triangle is created. Its hypotenuse is the slant height of the pyramid. Using the Pythagorean Theorem with the height and half of the length of the base as the legs of the right triangle, you can calculate the slant height. Using the Pythagorean Theorem and rounding to the nearest whole number value, the slant height is calculated to be about 436 feet.

Next, let's look at the Pyramid Arena as a net with all of the measurements that you know now. ### Pause and Reflect

How could nets help you determine the surface area of other figures?

Interactive popup. Assistance may be required.

If you know the net of a figure and its dimensions, then you can calculate the area of the relevant faces of the figure. ### Practice

For each of the figures below, determine the total surface area.

Interactive popup. Assistance may be required.

What shapes are the faces that are present in each net? What are the area formulas that you can use to determine the area of each of those shapes? 1. 2. Interactive popup. Assistance may be required. Check Your Answer This net is a triangular prism, which has two congruent triangular bases and 3 rectangular lateral faces.Area of Base=1 over 2 1 2 bh = 1 over 2 1 2 (3.5 cm)(3 cm) = 5.25 cm2Area of Lateral Faces= bh + bh+ bh= (8.6 cm)(3.5 cm) + (8.6 cm)(3.5 cm) +(8.6 cm) (3.5 cm)= 30.1 cm2 + 30.1 cm2 + 30.1 cm2 = 90.3 cm2 Surface Area= Area of Bases + Area of Lateral Faces = 2(5.25 cm2) + 90.3 cm2 = 100.8 cm2 Interactive popup. Assistance may be required. Check Your Answer  