MHB Calculating Total Area Under a Trapezoidal Curve for Water Tank Fill Time

AI Thread Summary
The area under the curve for the water tank fill time consists of a triangle and a rectangle. To calculate the area, a horizontal line at "100" and a vertical line at "2" are drawn, creating a right triangle with legs measuring 2 and 200, and a rectangle with width 2 and height 100. The area of the triangle is calculated, and if the combined area of the triangle and rectangle is less than 1000, this value is subtracted from 1000 to determine the required area for a second rectangle. The discussion emphasizes the need to find the width of this second rectangle to achieve the desired area. Overall, the focus is on accurately calculating the total area under the trapezoidal curve.
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sophbell said:
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The area represented under the curve is a triangle (up to t = 2 hours) plus a rectangle. How do you find the sum of that area?

-Dan
 
Draw a horizontal line at "100" all the way across. Draw a vertical line at "2" all the way up and down. That divides the area into a right triangle with one leg of length 2 and the other of length 200, a rectangle with width 2 and height 100, and another rectangle with height 300 and unknown width. What is the area of the triangle and the first rectangle?

If that is less than 1000, subtract if from 1000. How wide must the second rectangle be so that its area is that difference?
 
topsquark said:
The area represented under the curve is a triangle (up to t = 2 hours) plus a rectangle. How do you find the sum of that area?

-Dan

Surely it's a trapezium and a rectangle...
 

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