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Point C (0,p) lies on the y-axis between Q (0,12) and O (0,0) as shown. Determine an expression for the area of triangle ABC in terms of p. Your answer should be simplified as much as possible.    Thank you!!

 

 

 May 27, 2020
 #1
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One of the ways to find the area of triangle(ABC) is to find the area of trapezoid(OBAQ) and subtract the areas of 

triangle(AQC) and triangle(OBC).

 

The area of trapeoid(OBAQ)  =  ½·height·(base1 + base2)  =  ½·OQ·(OB+ QA)  =  ½·12·(12 + 2)  =  84

                          

The area of triangle(AQC)  =  ½·base·(height)  =  ½·AQ·(QC)  =  ½·2·(12 - p)  =  12 - p

 

The area of triangle(OBC)  =  ½·base·(height)  =  ½·OB·(OC)  =  ½·12·(p)  =  6p

 

Subtracting, we get:  triangle(ABC)  =  trapezoid(OBAQ) - triangle(AQC) - triangle(OBC)

                                                         =  84 - (12 - p) - (6p)

 

You can do the simplifying ... 

 May 28, 2020

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