Geometry is a continuation of the knowledge acquired within ShapesWe 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...