Video: Finding the Area of a Rectangular Object

A wall of a house has a length 𝑙 = 12 m and a height ℎ = 5.5 m, as shown in the diagram. What is the area of the wall to the nearest square metre?

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Video Transcript

A wall of a house has a length 𝑙 equals 12 metres and a height ℎ equals 5.5 metres, as shown in the diagram. What is the area of the wall to the nearest square metre?

Okay, so here’s our wall, and we’re told the length of this wall as well as its height. We’re told the length is 12 metres and the height of the wall is five and a half metres. To the nearest square metre, we want to solve for the area of this wall. If we label that area capital 𝐴, then it represents the entire interior space of this rectangle. And we know that this is a rectangle because, based on our diagram, all the sides of the shape are at right angles to one another. In order to solve for this area of the wall, let’s recall the mathematical formulation for the area of a rectangle. If we call that area 𝐴 sub 𝑟, then it’s equal to the length of a rectangle 𝑙 multiplied by its height ℎ.

By the way, another way to write this equation is 𝑏 times ℎ, where 𝑏 is the base of the rectangle. But here, since we have a length 𝑙 representing that same distance, we’ll use 𝑙 in our equation. So in general, the area of a rectangle is equal to its length times its height. And for our rectangle, this wall, that area is equal to the specific length and the specific height given multiplied together. When we substitute in the given values for 𝑙 and ℎ, we see that each one includes a number as well as a unit attached to that number. When we multiply the length times the height, we can deal with these two quantities separately. What we’ll do first is will multiply the numbers together and then second will combine the units.

So then we can write the area this way. It’s equal to 12 times 5.5. That’s the combination of the numbers. And then the units are metres times metres. If we multiply 12 by five and a half, that’s equal to exactly 66. And then if we multiply a metre by a metre, that’s equal to a metre squared. So we’ve combined both the numbers to give us 66 and the units to give us metre squared. Our question asked for the area of the wall to the nearest square metre. And looking at our results, we see that it’s written that way. So then the area of this wall is 66 metres squared.

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