Question Video: Finding the Area of a Composite Figure Involving Rectangles Mathematics • 6th Grade

Find the area of the given shape.

03:49

Video Transcript

Find the area of the given shape.

So in order to solve this problem, we in fact have a couple of different methods. And to help us use these methods, what we have are a couple of formulae. And the first one is that the area of a rectangle is equal to the length multiplied by the width. And the other one is the fact that the area of a square is equal to the side length squared. For the first method, what we can think of is the whole entire shape with two squares cut out. So what we’ve got is one large rectangle, which is 19 by 15. And then we’ve got two squares cut out, one four by four and the other eight by eight.

So first, what we do is calculate the total area of the whole rectangle. And this is 19 multiplied by 15, which is gonna be 285 centimeters squared. And a quick mental method we could’ve used to work this out is 20 multiplied by 15. Well, two 15s are 30, so 20 multiplied by 15 is 300. And then we just subtract 15 because we only want to multiply it by 19 in our problem. And 15 away from 300 is 285. Okay, great. So that’s our total area.

So now, if we were to call our small square 𝐴, then we can find the area of 𝐴, which is gonna be equal to four squared, which is equal to 16 centimeters squared. And then, the area of the square 𝐵 is gonna be equal to eight squared, which is gonna be equal to 64 centimeters squared. So great, we’ve now got the area of the total rectangle and the two squares. So now, if we want to find the total area of the shape, what we’re gonna do is 285 minus 16 minus 64, which is 285 minus 80. Which is gonna give us a final answer for the area of the shape of 205 centimeters squared.

However, we did mention that there’s a second method we could use. So we’re gonna have a look at that now. Now, for the second method, what we can do is divide our given shape up into different rectangles or squares. So what we’ve decided to do in this problem is divide it vertically into three rectangles. And now, what we can do is work out the area of each of these rectangles and add it together. However, to be able to do this, first what we need to do is write on some more dimensions.

So the first dimension we can write on is the height of our rectangle 𝐴. And that’s gonna be seven centimeters. And we could work that out because it’s 15, which is the total height, minus eight, which is equal to seven. And then if we want to find the width of our rectangle 𝐵, well, this is equal to seven centimeters. And that’s because it’s 19 centimeters, which is the total width, minus eight minus four, which equals seven. And then finally, we have the length of rectangle 𝐶. And this is 11 centimeters because this is 15, which is the total length or total height, minus four, which gives us 11.

So now, what we can do is work out the area of each of our rectangles. Well, the area of rectangle 𝐴 is gonna be equal to eight multiplied by seven, which is equal to 56 centimeters squared. Then the area of rectangle 𝐵 is gonna be equal to 15 multiplied by seven, which is 105 centimeters squared. And we get this because if you multiply seven by 10, that’s 70. Seven by five is 35. Add them together gives you 105. And then, finally, rectangle 𝐶 is just 11 multiplied by four, which is gonna be equal to 44 centimeters squared.

So therefore, the area of the given shape is gonna be equal to 56 plus 105 plus 44. So that’s all of our areas of the rectangles added together, which will give us an answer of 205 centimeters squared, which is the same answer we got from our first method.

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