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Mathematics-Online problems:

Interactive Problem 154: Areas of Triangles and Quadrilaterals

A B C D E F G H I J K L M N O P Q R S T U V W X Y Z
In the figure shown below, the points

$\displaystyle A_1 = (0,0),\quad A_2 = (1,0),\quad A_3 = (2,0),\quad A_4 = (3,0) $

are connected with the points

$\displaystyle B_1 = (0,3)$    and $\displaystyle \quad B_2 = (3,3)$

by straight lines.


\includegraphics[width=0.4\linewidth]{TdM_11_A2_bild}


Find the areas of the triangles and quadrilaterals with labels $ F_1,\ ...\,,\, F_7$ in the figure.


Answer:

Triangles:          
$ F_1 =$          $ F_2 =$          $ F_3 =$    
$ F_4 =$          $ F_5 =$        
               
Quadrilaterals:          
$ F_6 =$          $ F_7 =$        

(The results should be correct to 3 decimal places.)


   

(From: Mathematics Contest 2011)
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  automatically generated: 2/ 6/2018