We’re on problem 31. A sewing club is making a quilt consisting of 25 squares with its side of the square measuring 27 meters. Okay. And there’s going to be 25 of these. And they’re going to be 30 by 30. If the quilt has five rows and five columns, what is the parameter of the quilt? Okay. So let me draw that out. So let’s say this is – it has five rows and five columns. And they’re all squares. So, the quilt itself is going to be a square. It has five rows. So, one, two, three, four, and five; and then one, two, three, four, so that’s a five by five and each of these squares, their sides are 30, right, 30 centimeters. So, how long is this one side of this quilt going to be? It’s going to be 30 times 5, right? So, it’s going to be 150 centimeters. Same argument, that’s going to be 150 centimeters, that’s going to be 150 centimeters, right, 30 times 5. And this is going to be 150 centimeters. So the perimeter is 150 plus 150, plus 150, plus 150 and that’s 600. So that’s choice C.
32. The four sides of this figure will be folded up and taped to make a box. Fair enough. What will be the volume of the box? Okay. If there, we cut this out right now and we folded it along where I’m drawing these green lines, we got a box. And then I want to say, what’s the volume? Well volume is just the base times the height times the depth, right? So if I were to fold up this box, it’s going to look something like this. You’re going to have the base, which is this base right here. And this is what? One, two, three, four, five by one, two, three, four, five, so it’s a five by five base. And then each of the sides are going to be too high. If I fold this up, it’s going to be too high like that, right? If I write it one, two, three, well, it’s going to look like that if I folded this side up. This is side up, when I fold it up, it’s going to look like this, right, one, two, three, four, five. That side when I fold it up, it’s going to look like that. And this side, when I fold it up, it’s going to look like that, so one, two, three, four, and five. The big picture, the width is five, the depth is five and the height is two. So, the volume is 5 times five, is 25, times 2, which is equal to 50. And that’s choice A.
Problem 33. Let me – where’s 33? I think it’s on the next page. Okay. Let me copy and paste it. You just copy and paste the whole test. Okay. It says a classroom globe has a diameter of 18 inches. If I were to go from the center to the side, it’s 18 inches. Which of the following is approximate surface area in – oh, sorry, I just drew the radius – it has a diameter of 18 inches. This is 18, right? Which of the following is an approximate area in square inches of the globe?
In surface area, they give us the equation. They give it in terms of the radius, right? So if the diameter is 18, what’s the radius? The radius is half of the diameter. The radius is half of the diameter. So the radius is equal to 9. And we just plug that in here. So, the surface area is equal to 4 pi times the radius squared, times 9 squared. That’s equal 4 times 81 times pi, or 9 square is 81, so, it’s 3, 4 pi. And you actually multiply it out, so let’s see. 4 times 81 is, 4 time 80 is 320. Then we have 324 pi. And then if I were to guess this, this is going to be, right, look at all the choices, pi is more than 3, right? So this value is going to be more than, 3 times 3, 24. So it’s going to be around a thousand or a little bit, yeah, more than a thousand. And the only one that’s even close to that is D. but if you wanted to confirm that, you could multiply 3, 24 times 3.14, that is equal to 1017.4. All right.
Next problem. Problem 34. Oh I’ll copy and paste 34 and 35 at the same time. Let’s see. Okay, almost there. All right. Okay, let me – there you go. I’m going to put this there. And then, all right, ready to do it. The rectangle show below has a length of 20 meters and width of 10. So this is 10 and this is 20. I just picked that because this looks longer than that. Fair enough, that’s a 10 I drew and I looked at it like a 10. If the four triangles were removed from the rectangle as shown, what would be the area of the remaining figure? So what’s the area before I remove them? It’s 20 times 10, right? That’s here are the whole rectangle. So it’s 200, and then how much area am I removing? So, each of these triangles, – what is its area? It is base times height times one half. That’s the area of a triangle, right? Because if you’ve adjusted base times height, you’d be figuring out the area of this little rectangle there. So the area of this is 4 times 4 is 16, times one half, which is8. This is going to be 8. This one’s going to be 8.S o we’re moving four 8’s from this area. So we’re moving 32. So, minus 32, and that’s what, 168. So that’s choice C.
Problem 35. If RSTW is a rhombus, what is the area – so rhombus tells us that all the sides are equal and they’re parallel – what is the area of WXT? So, this right here. Okay. So this is something that you maybe may or may not have learned about a rhombus, but its diagonals actually intersect at a perpendicular line. And let me see what else we can – see, this is 16 degrees, so this is 30 degrees. Let’s see what we can get from this. This is 12. Then this is 12. Oh, okay. I see where they’re going with this. So if this is 90 degrees, this is 90 degrees. I mean it’s a rhombus; all the sides are the same, right? If this 60, this is 90, this has to be 30 degrees, right? This has to be 30 degrees. And then you can actually make a very strong argument that these are similar triangles, whatever length this is, that’s the same length because this is a parallelogram and the diagonals bisect each other. This side is equal to that side. That side is equal to this side. So these are congruent triangles. So this is also going to be 60 degrees. This is going to be 30. But if you have a 60, let me do it another color – If you have a 60-60-60 triangle, all of the angles are 60 degrees. You’re dealing with an equilateral triangle. So that tells you that all the sides are the same. So, this side is 12. That side is 12. This side right here also, has to be 12. That side here also, has to be 12. If that whole side is 12, what’s this length? We already know that in a parallelogram, the diagonals bisect each other. So this length is 6 and this length is 6. Fair enough. Now let’s see. If each of these lengths are 6, can we figure out what this height is equal to? Because if we know the base and the height, we’re ready to figure out the area of a triangle. So let’s see if we can use a Pythagorean. If we call this x, we could say x squared plus 6 squared, plus 36 is equal to 12 squared, is equal to 144. And we could say that x squared is equal to – what’s 144 minus 36? That’s 108. I want to say yea, 108. So x squared is equal to 108. X is equal to the square root of 108. And I can simplify that more because 9 goes into 108. Right, 9 goes into 108 12 times, right? Now, let me do that. So x is equal to the square root of 9 times 12, that’s 108. So that’s equal to the square root of 9 times the square root of 12. Well the square root of 12, see that equal to 3 times the square root of 12. Square root of 12 is the same thing as the square root of3 times the square root of 4, right? Square of 4 is 2. So, that’s 2 times 3 is 6 square roots of 3. Right, this is 36 times 3. We could have said this is equal to the square root of 36 times the square root of 3. You can’t see what I just wrote there. Times the square root of 3, right? All right. So, 6 square roots of 3. That’s this side.
So what’s the area of this triangle right there. That’s one half times this base times 6 times 6 square roots of 3. So that’s one half times 6 is 3, time 6 square roots of 3, is 18 square roots of 3. Now that’s just this triangle. This triangle is congruent to this triangle, so we’ll have the same area. And you can make the same argument that all of these triangles are congruent. So the area of this entire rhombus is going to be 4 times this, right? If I’m looking at – right, It’s going to be 4 times – is that what they wanted? Oh. No. No. They wanted the area of WXT. That’s what we just figure out. They didn’t want the area of the whole rhombus. They want just the area of this triangle right there, which we just figured out, which is 18 square roots of 3.
I’m trying to think if there’s a simpler way of doing this. There might be some formula for the equation for the area of the rhombus that I’ve forgotten in my memory, but we we’re able to reprove. And that’s actually better to actually come from basic principles. Anyway, I’ll see you in the next video.
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