11.3 & 11.4

Today in class we covered two sections: 11.3 and 11.4.

11.3 was about the area of a trapezoid. To find the area of the trapezoid, use this formula (in this formula, the a and b stand for the base 1 and base 2):





We learned that the formula comes from a few places, such as the ones shown below:

 
You can move the triangles on the sides up to the top of the trapezoid to create a rectangle. 

Here, it shows how the trapezoid the area formula is made. 

• The area of the rectangle is b₁h.
• The area of the triangle on the left side is ½xh.
• The area of the triangle on the right side
  is ½(b₂ – b₁ – x) × h = ½b₂h – ½b₁h – ½xh.
• The combined area of the three pieces, then,
  is b₁h + ½xh + ½b₂h – ½b₁h – ½xh, which simplifies to ½b₁h + ½b₂h. This further simplifies to ½(b₁ + b₂) h, which is the trapezoid area formula. 

(All of this info I found at http://illuminations.nctm.org/LessonDetail.aspx?ID=L580)

Another very helpful website is http://www.mathopenref.com/trapezoidarea.html

On it, you can change the base and the height in an interactive trapezoid. It also clearly explains the formula and has videos you can watch.

Next, we went on to 11.4, which was the area of kites and/or rhombi.
To the area of a kite or a rhombus, you use the formula A= ½ d₁d₂ 
This formula comes from the fact that a rectangle can be drawn around a kite or rhombus and that the kite or the rhombus can be "cut up" and then turned into a rectangle that has an area one half of the big rectangle.

That's about it! I hope that everyone loves our blog at the conference thing. Also, LOST THE GAME :)


-Jessica