Chapter 11: Area, A.K.A The one before THE Curve

Area is measured in square units and is one of the most important features of Geometry.

Those are all the Formulas for the area of shapes, except for the kite which will be mentioned later on.

However, there is more to area than just formulas. For example the trapezoid comes with a few nifty little theorems as well.

Trapezoid: Every trapezoid has a median. The median of a trapezoid is the segment connecting the midpoints of the non parallel sides. The length of a median is found multiplying the sum of the parallel sides by 1/2.

This equation is represented as

m= (a+b)/2

also, the area of a trapezoid can be found by multiplying the median by the trapezoids height.

Lastly, the median of a trapezoid bisects the diagonal of the trapezoid, providing a basis for some interesting questions from Mr. Wilhelm.

The area of a kite is

A=1/2d^1,d^2

The diagonals of a kite form a right angle, and also sides d and a are congruent as are sides c and b. Lastly a kite has one pair of congruent angles, these angles are the ones that d^2 runs through.

In a rhombus, the diagonals form right angles, and bisect the other diagonals. Also all sides are congruent.

Next are the areas of regular polygons. For an equilateral triangle the formula is

A= ¼(s²⋅√3)

The area of any regular polygon is ½ apothem ⋅height

A=½ap

KEY SOLUTION TO HEXAGONAL FIGURES AND EQUILATERAL TRIANGLES!!! ITS CALLED 30-60-90 TRIANGLES!!!

Picture TIME

I don't know the exact equation but a segment is a sector minus its inner triangle.

As far as ratios go if its area you square the equation and for volume you cube the equation.

Oh and a median of a triangle divides the triangle into two triangles with equal areas.

Lastly Hero's and Brahmagupta's Formulas

first, Hero's.

next, brahmaguptas

Now For a Trip Down Memory Lane

First, Proofs.

Now that I think about it all we really did 1st tri were proofs soo...

HEY its our book.

I'd like to give a shout-out to Mr. Wilhelm, the greatest teacher ever, and a kudos to my fellow bloggers, wheel spinners, book lickers, trigons, game losers, and applauders. Thank you all for making this honors geometry class

a little more enjoyable and interesting than most other classes,

Oran Lieberman

10.3

Hello, friends!
We've gone through the entire class for blogs, so logically it must be my duty to once again do the first blog post.

Today we learned a couple of things.
1) there are 3 types of arcs


     a) semicircles- 180 degree arcs (requires 3 points to name and identify)

     b) major arcs- greater than 180 degrees (requires 3 points to name and identify)

     c) minor arcs- less than 180 degrees (requires 2 points to name and identify)


2) Congruent arcs on different circles implies that the circles are congruent.
     a) to be congruent, both the angle measure and the length must be the same.

3) Congruent chords implies congruent arcs which implies congruent central angles which implies congruent chords. Basically, if you have a congruent Chord, you can prove the other two (central angles and arcs) congruent. If you have one you can prove the other two. They're biconditional.

Alright, gang. I'm off  for Orlando. Be good for Mr. Wilhelm and do 10 nice things a day for the next couple days till break. It'll make you feel good.
Shane McPartlin.
P.S.

                     March 6th.                                                                Get pumped.