7: Geometry

Last updated

Nov 6, 2023
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- 6.7: Find the Equation of a Line
- 7.1: Perimeter and Circumference

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7.1: Perimeter and Circumference
A polygon is a closed geometric figure with straight sides. Common polygons include triangles, squares, rectangles, parallelograms, trapezoids, pentagons, hexagons, octagons… The perimeter of a polygon is the distance around the outside. In general, to find the perimeter of a polygon, you can add up the lengths of all of its sides.
7.2: Area of Polygons and Circles
We have seen that the perimeter of a polygon is the distance around the outside. Perimeter is a length, which is one-dimensional, and so it is measured in linear units (feet, centimeters, miles, etc.). The area of a polygon is the amount of two-dimensional space inside the polygon, and it is measured in square units: square feet, square centimeters, square miles, etc.
7.3: Composite Figures
Many objects have odd shapes made up of simpler shapes. A composite figure is a geometric figure which is formed by—or composed of—two or more basic geometric figures. We will look at a handful of fairly simple examples, but this concept can of course be extended to much more complicated figures.
7.4: Surface Area of Common Solids
In this module, we will look the surface areas of some common solids. (We will look at volume in a later module.) Surface area is what it sounds like: it’s the sum of the areas of all of the outer surfaces of the solid. When you are struggling to wrap a present because your sheet of wrapping paper isn’t quite big enough, you are dealing with surface area.
7.5: Volume of Common Solids
The surface area of a solid is the sum of the areas of all its faces; therefore, surface area is two-dimensional and measured in square units. The volume is the amount of space inside the solid. Volume is three-dimensional, measured in cubic units. You can imagine the volume as the number of cubes required to completely fill up the solid.
7.6: Pyramids and Cones
This page covers the geometry of pyramids and cones, detailing their volume and surface area calculations. It defines pyramids by their polygonal bases and triangular faces, and cones by their circular base. The formulas show that pyramids and cones have one-third the volume of their corresponding prisms and cylinders. Exercises focus on calculating volume and surface areas, and a practical exercise involves calculating the volume of a propane tank.

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