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In rectangle $WXYZ$, $A$ is on side $\overline{WX}$, $B$ is on side $\overline{YZ}$, and $C$ is on side $\overline{XY}$.  If $AX = 2$, $CX = 24$, $CY = 3$, $BY = 3$, then find the area of triangle $ABC$.

 Dec 20, 2023
 #1
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W           A    2   X

                        

                        24                 

 

                         C

                         3

Z       B     3      Y

 

AXYB is a  trapezoid

Area =  (1/2) (XC + CY) (AX + BY) = (1/2)  (24 + 3) ( 2 + 3)  =   135/2 = 67.5

 

Triangle AXC  has area   (1/2((2* 24) =  12

Triangle CYB has area     (1/2) (3 * 3) = 4.5

 

[ABC ] =  [ AYXB ] - [ AXC ] - [ CYB ]  =   67.5 - 12 - 4.5  =   51

 

 

cool cool cool

 Dec 20, 2023

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