### Geometry

 Geometry is a continuation of the knowledge acquired within Shapes We have already learned about several two-dimensional shapes.   We now have the skills to calculate the perimeter of any polygon.  We should also have a firm understanding of the different formulas needed to calculate the area of any shape and the circumference of a circle.   (Remember that Pi = 3.14159...) Please note that  within every triangle:  all angles of any triangle add up to 180° Now the time has come to add a new dimension.  The third dimension, depth.  Three dimensional objects are often referred to as solids. There are two common calculations with 3D objects, surface area and volume (capacity)                    a cube is the most common term for a where all sides are equal       a cube's surface area is the area of one side of the cube (H x W) multiplied by 6     the volume of a square can be found by multiplying the height, width, and depth                                                             or   V = H x W x D a rectangular solid or box or both terms common to this 3D shape  the surface area can be found by adding twice the area of each non-opposing sides     or to use the example given:  2(H x W) + 2(H x D) + 2(D x W)                                                         2(2 x 4) + 2(2 x 3) + 2(3 x 4) the volume can be found much like that of a cube   V = H x W x D  a sphere or ball is a three-dimensional circle   the surface area of a sphere can be found by multiplying 4 x ( π x r2 )        or to use the example given:  4 (π x 142)  the volume of a sphere can be found by using the following formula                           V =  4  x π x r3                                   3             a cylinder is the most common term for this 'can-like' shape             to find the surface area of a cylinder, add both circle areas to the radius times the height                                      or  surface area = 2(π x r2) x r x h             the volume of a cylinder can be found using the following formula                                                V = h x π x r2             (think of this as one circle stacked atop another for the height of the cylinder)                  a cone is the term used for this shape regardless of it's orientation (facing up or down)                    the surface area of a cone can be found by adding ( π x r2 ) with (pi x height x length of side)                               the volume of a cone can be found using the following formula                                                    V = ⅓ x h x π x r2       a pyramid is the name used for this three-dimensional object       the surface area of a pyramid can be found by adding the area of the square base to                                                                                                    the areas of each triangle side                    or      surface area = b2 + 2 x base x length of side              the volume of a pyramid can be found using the following formula                                        V = ⅓ x b x h These are the most basic shapes you will encounter.  However, three-dimensional shapes can be found in many other different forms.                                                                                               Such as : We will now take a closer look at angles and their attributes. As shown in this image,  complementary angles are two angles who's sum add up to make a right angle (90°)      Complementary Angles As shown in this example,  supplementary angles are two angles who's sum add up to make a straight line (180°)                           ∠ DEF + ∠ ABC = 180° Use this figure to refer to similarities between angles, and note that when two parallel lines are intersected by a straight line the following is true:       opposite angles are equal          b = c = f = g              and        a = d = e = h more coming soon...