A rectangular field with dimensions sixty-eight metres and forty-three metres is surrounded by a fence. The field contains a square playground with side length thirteen metres that also has a fence around it. Calculate the total length of fence around the field and the playground.
Now we’ve been given a little diagram. So we can annotate that diagram and write the dimensions on there. The field is rectangular. And a rectangle is a four-sided shape that has four right angles and the opposite sides of equal length. So we can now write the dimensions in there because we can see which is the longer side and which is the shorter side. So that side is sixty-eight metres and the other side is forty-three metres. Now the opposite sides are also the same length, so I just write those down as well. And the playground in the middle is a square. A square is a special type of rectangle. So it’s also got four sides, it’s also got four right angles, and its opposite sides are also equal. But the additional thing with the square is in fact, not only are the opposite side equal but all four sides are equal in length. So I can mark those lengths on my diagram as well.
All that remains now, is first to calculate the total length of fence around the field and the playground. So we’ve got to work out the perimeter of the field, the perimeter of the playground, and add them together. Now the perimeter of the field is this length plus this length plus this length plus this length, so that’s two lots of sixty-eight metres and two lots of forty-three metres. And the perimeter of the playground is this length plus this length plus this length plus this length, so that is four times thirteen metres.
Now I’m gonna use the distributive property to write this bit of our equation out slightly differently. Two times sixty-eight plus two times forty-three is the same as two times sixty-eight plus forty-three. And sixty-eight plus forty-three, well sixty plus forty is a hundred and eight plus three is eleven, so that’s a hundred and eleven. And two times a hundred and eleven is two hundred and twenty-two. But look, I’ve only calculated the first half of this. I also need to calculate the second half. Four times thirteen, well that’s the same as two times thirteen, and then times that by two. So two times thirteen is twenty-six and times that by two, I get fifty-two.
So the total length of fence is two hundred and twenty-two plus fifty-two, which is two hundred and seventy-four. Now it’s important to think about the units. All the dimensions we were given were in metres, so our units are metres. And there we have it, the answer is two hundred and seventy-four metres. And we’ve just got time to go back and correct our spelling mistake. We spelt perimeter wrong. Instead of “perimiter”, it should be perimeter, perimeter.