Video: Using Areas of Rectangles

Calculate the area of the shaded region.

03:01

Video Transcript

Calculate the area of the shaded region.

So to calculate the area of the shaded region, what we’re gonna be looking at is rectangles. So first of all, we’re going to have a look at what is the formula for the area of a rectangle. Well, the formula for the area of a rectangle is the area is equal to the length multiplied by the width. And we can see that, in our question, we’ve got two rectangles. We’ve got a large rectangle. And then we’ve got the smaller rectangle within it. And I’ve labelled them 𝐴 and 𝐵. And we can see that the shaded area is gonna be equal to rectangle 𝐵 minus rectangle 𝐴. And that’s because if we have the total rectangle and remove the part that’s rectangle 𝐴, we’re left with the shaded area.

So we’re gonna start with the area of rectangle 𝐴. And this is gonna be equal to eight multiplied by five. And that’s because eight is our length, eight meters. And five is our width, five meters. And this is gonna give us an answer of 40 meters squared. So great. We found the area of rectangle 𝐴. And then, for rectangle 𝐵, what we’re gonna have is 28, because 28 meters is length, multiplied by 30, because 13 meters is the width. And it’s gonna give us a final answer of 364 meters squared for the area of rectangle 𝐵. And we could do that using a calculator. Or we could do it the written method. And I’ve got one here using the column method. So you have 28 multiplied by 13.

So first of all, we do three multiplied by eight, which is 24. So we carry the two into the tens column and put four in the units column. And then we have three multiplied by two. Or really, it’s three multiplied by 20, which gives us six or 60. And six add two gives us eight. So then, we get eight in the tens column. So then, we’ve got 84. Then next, what we’re gonna do is multiply the one from the 13. So the 10 by the eight and the two. So first of all, we’re gonna put a zero in the units column. And that’s because, because we’re multiplying by 10. There aren’t gonna be any units.

First of all, we’ve got one multiplied by eight or 10 multiplied by eight, which gives us 80. So we put an eight in the tens column. Then we’ve got one multiplied by two. Or really, it’s gonna be 10 multiplied by 20. Well, this will give us 200. So we put a two in the hundreds column. And now all we need to do is add the two values together. So 84 and 280. Four and zero is four. Eight add eight is 16. So six in tens column, one in the hundreds column. And then, two add the one that we carried gives us three. So we get 364, which is what we got before. So great. We’ve got the area of rectangle 𝐴, the area of rectangle 𝐵. So now let’s find the shaded area.

Well, the shaded area is gonna be equal to 364, cause that’s the area of rectangle 𝐵, minus 40, cause that’s the area of rectangle 𝐴. Which will give us a final answer for the question of 324 meters squared.

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