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!!
+23245 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 ...
