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Numerade Educator

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Problem 48 Medium Difficulty

The widths (in meters) of a kidney-shaped swimming pool were measured at 2-meter intervals as indicated in the figure. Use the Midpoint Rule to estimate the area of the pool.

Answer

$91.2 \mathrm{~m}^{2}$

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Video Transcript

the wits in meters of a kidney shaped swimming pool where measured at two meter intervals, as indicated in the figure he's the midpoint rule to estimate the area of the pool. Okay, first of all, what did they tell us? They tell us that Ah, the the wits were measured in two meter intervals. So that means that the distance between each of these measurements here let's he's a pen. So So this distance here is two meters this distance. Here's two meters. Each of these distances is two meters. Okay, now we want to use the midpoint rule. So what are we going to do? So basically, what we're going to do is we're going to determine the area by approximating it. Ah, by cutting this pull up in two different regions and we're going to approximate each of these areas separately using the midpoint so area is equal to. So let's look at this first region here. The mid point has a with in meters of 6.2 6.2 meters multiplied by this horizontal distance here. So what is that distance it's going to be? It's double the distance between measurements. So this is going to be a total of four meters. In fact, this is going to be true for each of these four meters, four meters and four meters. Okay, So the area of the first part of the pool can be approximated as 6.2 meters comes four meters plus the area of the second region is 6.8 is coming from the midpoint of the second region multiplied by the by the width of this region, four meters plus 5.0 meters multiplied again by four and finally 4.8 meters multiplied by four. So after we compute all of this, we get the total area well, an approximation for the area has 91.2 meters squared a meter squared coming from the fact that our units his meter's times meters For each of these, uh um components of the sun