Geometry

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...