12 Geometry Review
Example 12.1 (Activity: Market tent) The Taos Farmers Market sets up a rectangular tent that is 40 feet long and 15 feet wide. What is the perimeter of the tent’s footprint? What is the area of the floor space inside the tent?
\(P = 2(40) + 2(15) = 80 + 30 = 110\) feet. \(A = 40 \cdot 15 = 600\) square feet.
Example 12.2 (Activity: Reflecting pool) A circular reflecting pool at a Taos resort has a diameter of 20 feet. What is the circumference of the pool? What is the area of the pool’s surface?
\(r = 20 \div 2 = 10\) ft. \(C = 2\pi(10) = 20\pi \approx 62.83\) feet. \(A = \pi(10)^2 = 100\pi \approx 314.16\) square feet.
Example 12.3 (Activity: Garden triangle) A triangular section of a community garden at UNM-Taos has legs of 12 feet and 5 feet. Is the longest side of this triangle exactly 13 feet? Show your work using the Pythagorean theorem.
Check: \(12^2 + 5^2 = 144 + 25 = 169 = 13^2\). Yes, the longest side is exactly 13 feet.
Example 12.4 (Activity: Ranch shed) A storage shed at a Taos ranch is 10 feet long, 8 feet wide, and 7 feet tall. What is the volume of the shed? How many square feet of material are needed to cover all six sides?
\(V = 10 \cdot 8 \cdot 7 = 560\) cubic feet. \(SA = 2(10)(7) + 2(10)(8) + 2(8)(7) = 140 + 160 + 112 = 412\) square feet.
Example 12.5 (Activity: Mosaic tile) A circular mosaic tile at a Santa Fe studio has a circumference of approximately 37.70 inches. What is the radius of the tile? What is the area of the tile?
\(37.70 = 2\pi r \Rightarrow r = \dfrac{37.70}{2\pi} \approx 6\) inches. \(A = \pi(6)^2 = 36\pi \approx 113.10\) square inches.