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Find the perlmeter and area of the following composite figure:34 f34 f32 f 32 f10 f1 f10 p0 fiPerimeterfeet (If needed; enter answer t0 declmal placeArensquare feet...

Question

Find the perlmeter and area of the following composite figure:34 f34 f32 f 32 f10 f1 f10 p0 fiPerimeterfeet (If needed; enter answer t0 declmal placeArensquare feet (If nceded enter answer [0 decimal place )NOTE: Figures are NOT to scale

Find the perlmeter and area of the following composite figure: 34 f 34 f 32 f 32 f 10 f 1 f 10 p 0 fi Perimeter feet (If needed; enter answer t0 declmal place Aren square feet (If nceded enter answer [0 decimal place ) NOTE: Figures are NOT to scale



Answers

Find the surface area of each composite figure. Round to the nearest tenth. (figure not copy)

To find the surface area of this composite figure. Let's think about one exactly at his. We have a solid cylinder, and inside it is a block. We want to remove that block. So imagine you're looking down a tube. This will give you an idea of what the surface area is gonna look like. You're looking down the tube. It's a circle, which would be the top of the cylinder, and inside it we have a rectangular block. So the surface area we're looking at is going to be the entire surface outside, which would be your cylinder, plus the surface that remains on the inside upon removing that block. So we need to have this part of our rectangular prism accounted for, and that's going to be its lateral area. The lateral area of the bloc would be all of its lateral surfaces Here inside, we also need to account for when we remove that block, it's leaving a hole in the cylinder, so we need to subtract out the area of the bases from our block. So when we're writing our formulas, we're going to have the entire surface area of the cylinder. Add to it. The lateral area of our rectangular prism and then subtract from it the base areas of the rectangular prism. So total surface area is the surface area of the cylinder, added to it the lateral area of the prism and subtract the base area of the prism, which would be are to be the prison. So that's our plan. Let's start with our cylinder. Surface area of a cylinder is equal to two pi h r plus two pi r squared. Now remember, this is the entire surface area. We know that H is 14 that was given an R was also given at 14. Substituting these values we have. Our surface area is equal to two times pi times 14 times 14 plus two pi 14 squared. So this is going to simplify to 14 squared times two is 392 pi, and again we have 14 squared times to 392 pi Roman numbers a little backwards there. Total surface area of our cylinder is 784 pi R units or feed. So let's not forget those and then hold on to that value for a little bit. We're gonna move over to our prism. To find the lateral area of the prism, we need the perimeter of the base times its height. While the perimeter is twice the length plus twice the width, we know the length and the width those air given If we look at her diagram here, whips we have a length of looks like 14 and a width of six were also given the height. It's the exact same height is our cylinder. So age is equal to 14 substituting these values two times 14 plus two times six our perimeter times the height. So the perimeter is 28 12 which is 40 times 14. Is our height total surface or sorry. Total lateral area of our printable. Our prism is going to be 560 square feet and just one more thing to account for. And that is the subtraction of the base area of our prism. That inside part, that we're pulling out because now we've created a whole. So the base of the prism is going to be twice the length times the wits as before. Length is 14 with this six. So we're gonna have our base is equal to 14 lips two times 14 times. Six. When we simplify, this is 168 square feet, and then we need to put it all together. Total surface area is the surface area of our cylinder 784 pie, plus the lateral area of our rectangular prism, minus the base area of the rectangular prisms. Using our calculator 784 pi plus 560 minus 168 it's approximately 200 e. 2855 0.0 square feet.

Let's find the surface area of the composite figure. I've drawn a picture for reference, but I'm going to describe what that picture is that we have a better idea of what the surface area is going to be a result of. So we have imagined a solid triangular prism. The first thing I want to notice is thesis. Ides of our triangle are 68 10 and this is a very special right triangle. 2345 right triangle, which is super helpful. So I'm just gonna indicate that this is a right triangle first with a high pot News 10 and then now imagine we're taking a cylinder, removing it from the center of this solid triangular prism. The cylinder is the full length of the prison, so we need to account for the surface area it leaves behind once it's removed. So the plan for finding the surface area of this prism we take the total surface area of the triangle triangular prism, add to it the lateral area of the cylinder and then remove the base area of the cylinder because once we remove the cylinder, it's leaving an opening at the top and bottom of that prism. So our plan total surface area will be equal to the surface area of the triangular prism plus the lateral area of the cylinder. Yeah, minus the base area. Have the cylinder. Now, keeping in mind there are two base areas. We're gonna have to make sure we account for that. Let's start with the prism. And we know the surface area is equal to the perimeter of the base times the height plus twice the base area. Our perimeter is going to be 10 plus eight plus six, which is 24. The area of the base is equal to half the base times the height, which is equal to half of six times eight, giving us 24 and then the height is equal to nine. So if we substitute these values in, we have a surface area of 24 times nine plus two times 24 264 square centimetres. Now let's move on to the lateral area of the cylinder. Lateral area is equal. Teoh two pi times the height of the cylinder times the radius. We know the height is nine and we know the radius is too substituting these values. We have two times pi times nine times two for a total lateral area of 36 pie centimeter square. And then finally our base area. So we're gonna have two of them, which is two times pi r squared. We know the radius is too. Two pi times two squared. Our base area is ate pie centimeter square. Now let's put all of that back together. To find the total surface area, we're going to take the surface area of the triangular Prism 264. Add to it the lateral area of our cylinder 36 tie and subtract the base area of our cylinder. This gives us a total surface area rounded to the nearest 10th of 352.0 square centimeters.

Let's find the surface area of the composite figure shown. We have a square prism that is two foot by two foot by half a foot and attached to it is a cylinder that is two feet tall, with a diameter of one foot. So the plan for this is to find the total surface area, which is the area of each surface. What we need to make sure we're aware of is the cylinder. When it's attached to the prism, we need to make sure we do not include that surface of the cylinder, because it's like sitting on top of the prism. So what we're going to do to find the total surface area is we're going to start by finding the total surface area of the prism we're gonna add to it the lateral area of the cylinder. So it's the outside of the cylinder, not including the bases. And then, since we still have one surface of the cylinder exposed down here on the bottom, we're gonna include that as well. So it's going to be 11 base area of the cylinder. So that's our plan, and now we have to do is right out the formulas for each substitute, the values were given and then simplify. Let's start with the prism surface area of the prism is the perimeter of the base times Height plus the area of the basis were given two feet by two feet for the base of our square, so the perimeter is going to be equal to four times to, which is eight. The height is given at 0.5 in the area of the base is equal to length times width, and that's two times two, which is for substituting all of these in and we have a surface area of eight times 25 plus two times for four plus. It gives us a surface area of 12 square feet moving on to the lateral area of the cylinder. Lateral area is equal to two pi R h. We're given the diameter as one foot diameter is equal to two are, so we go ahead and substitute one in for two are which leaves us with the lateral area being equal to high times. The two are times the height, which is two feet. Lateral area of the cylinder is two pi square feet and then finally will move on to the base area of cylinder. Remember, we only need one of them because the 2nd 1 is kind of hidden when it's connected to our prism. So the base area is equal to pi R squared, since our diameter is one foot, the radius, this 0.5 feet, substituting and simplifying that value. We have a base area that is equal 2.25 pi square feet now, putting all of these values into our original pant plan. To find the surface area we've got. Total surface area is equal to 12 feet plus or square feet, two pi square feet. Plus I went to five pi square feet, rounding to the nearest 10th. We have a surface area that is approximately 19.1 square feet.

The first thing I did is I plotted points D E and F in according it plain, and I connected them to create a triangle. To find the pyramid of a triangle, they need to know the length of each side. Let's start with Side E. D. Since E. D is a vertical segment, we can Con Backs is between points e N d to find its length, account the boxes and we get E D equals five units. Next, we're going to use the distance formula to find E F and F D. The distance formula is in the top right corner of the screen. E f equals. Let's use the coordinates of points E and F and plug them into the distance formula. First, we're using the Exco Ordinance to minus negative too, to the second power. Plus. Now we're going to use the Y coordinates negative one minus three to the second power. Let's simplify the expression under the square root to minus negative to its four. So we have four to the second power of plus negative one minus three is negative for, so we have negative for to the second power four to the second power is 16 and negative for to the second. Power is also 16 16 plus 16 study too. So we have squared of 32. We can use a calculator to figure out squared of 32 around the answer to the nearest 10th. So we get 5.7 units, we will repeat the process to find the length of the F, They're going to use the coordinates of points D and F and plug them into the distance formula to minus negative, too, to the second power, plus nobody one minus negative, too. To the second power, we simplify the expression under the square root. Tu minus negative two is four. So we have four to the second power. Plus never anyone minus negative two is one to the second power four to the second Power is 16 and want to the second power is one 16 plus one is 17. We can figure out the square root of 17 on a calculator and round the answer to the nearest 10th and we get about 4.1 units. Now we confined the perimeter by adding all sides together so the perimeter equals five Cost 5.7 plus 4.1, which equals 14.8 units. Next we will need to find the area of the triangle. The formula for the area of a triangle is based on site over to we need to draw a height of this triangle. The easiest way to draw height is to either draw vertical or horizontal Linus, if possible in this triangle, weaken draw. Ah, height starting at point F and perpendicular to side e. D. This way we created a height that is a horizontal line. This way we can count boxes to calculate the length of the height. If you count the boxes between point F and where the height hits E. D. That is four units, so I'm going to scroll down to write down this information. So the height of the triangle, so the height of the triangle is four units. The base of the triangle is the side that the height is crossing, and that is E E. D, which were found previously that it's five units long. The formula for the area is base times height over to let's plug in the numbers. Into this formula, we have five times for over two, five times four is 20. So we have 20 over to which is 10. So the area of this triangle is 10 square units.


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