Question

Can someone help me find the height of these inscribed rectangles. I know the width is 1...

Answer 1

@ganeshie8 @thomaster

Answer 2

@mathslover @amistre64

Answer 3

It is hard to read off the height from the graph, but you can use the equation they give you
y = 3x-4

Answer 4

For example, the red rectangle starts at 2. at x=2, y (the height) is 3*2-4= 6-4=2

Answer 5

To get the total area I add the area of all 3 rectangles together?

Answer 6

Yes. You are "estimating" the area of the triangle by adding up the areas of the 3 rectangles.

Answer 7

Can the whole part be treated as a trapezium? And then using the formula for calculating the area of trapezium ?

Answer 8

the area of each rectangle is width * height
width (as you said) is 1, so area = y of each rectangle

Answer 9

If it is treated as a trapezium then we can solve it like this :



\(\textbf{Area of Trapezium } \quad = \sf{ \cfrac{(a+b)\times h}{2} \\ }\)

a and b are the lengths of parallel sides and h is the height of the trapezium

h = BC = 3 units
a = AB = 2 units
b = CD = 11 units

Answer 10

but am i finiding the total area of all the rectangles? or just for each one.

Answer 11

@phi

Answer 12

the question says: Use the area of the 3 inscribed rectangles to estimate the area of the triangle.

That means find the area of each rectangle and add them up. The sum will be a (low) estimate of the area of the triangle.

Answer 13

you should first find the heights of each rectangle:
if you use the equation of the line (which forms the triangle)
y = 3x-4
at x=2 , y = 2
x=3, y= 5
x=4, y= 8

Answer 14

Thanks.

Answer 15

The estimate is obviously not very good... but in calculus they use this exact idea, but with *lots* of *very skinny* rectangles... it turns out to work very well for find the area under a curve.

Answer 16

Yes, as per the question, you need to just use the 3 rectangles. It will make difference of 4.5 sq. units to the original area.