Rose’s garden is in the shape of a trapezoid. If the height of the trapezoid is 16 m, one base is 20 m, and the area is 224 m^2, find the length of the other base.
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The formula for the area of a trapezoid is:\n\nArea = height/2 * (base1 + base2)\n\nso plugging in the known values:\n\n224 = 16/2 * (20 + base2)\n224 = 8 * (20 + base2)\n28 = (20 + base2)\n28 = 20 + base2\n8 = base2\n\nSo the other base is 8 meters.
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V=1/2(b1+b2)*h*w  where b1 and b2 are the two parallel sides of the trapezoid and h is the height and w is the width.
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1. A sphere with a diameter of 16 mm has the same surface area as the total surface area of a right cylinder with the base diameter equal to the sphere diameter. how high is the cylinder?\nA (sphere)=4*pi*r^2=4*pi*8^2=256*pi mm^2\nA cylinder=2*pi*r^2+2*pi*r*h==128*pi+16*pi*h\nA sphere=A cyl\n256*pi=128*pi+16*pi*h\n128*pi=16*pi*h\n8=h\nheight is 8 mm\n\n2. find the volume of a frustum of a right pyramid whose lower base is a square with a side 5 in. , whose upper base is a square with a side 3 in. , and whose altitude is 12 in.?\n\nB1 area=25in^2\nB2 area=9in^2\naltitude=3\nV=1/3(3)(25+15+9)=49in^2\n\n3. The figure formed by the intersection of a solid with a plane parallel to the base of the solid is congruent to the base if the solid is a........? \n\nprism
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A circle has 360 degrees. Now imagine that from the icosagon you can make 20 equally-sized triangles. The angle made by each triangle is 360/20=18 degrees. The other two angles of each triangle are both 81 degrees.\n\nThe basic formula for the area of a triangle is 1/2 base x height. How do we find these? Well, imagine that from each of the 20 triangles we make two additional right triangles. In doing this we know several things:\n\n-The hypotenuse is equal to 6.5 cm (the radius).\n-The angles of the smaller triangle are now 9 degrees, 81 degrees, and 90 degrees.\n-The sine of 9 degrees is equal to the opposite side divided by the hypotenuse. If we multiply this value by 6.6 we get the length of the opposite side ("1/2 base").\n-The sine of 81 degrees multiplied by 6.5 gives us the "height".\n-Once you compute each value (1/2 base and height) you multiply them by each other and you get the area of the triangle.\n-Multiply the area of that triangle by 20, since you have 20 of them. Voila.
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I am assuming you mean something like a round flower pot, where the base is smaller than the top.  You are saying the bottom has a diameter of 17 inches and the top has a diameter of 34 inches, with a height of 34 inches (not the slant).\n\nIs this correct?  I've also heard this called a truncated cone.  The formulas for volume is given below:\n\nHeight: h\nRadius of bases: r, R\nVolume: V\n\nV = Pi(R^2+rR+r^2)h/3\n\nSo plugging in your values (don't forget to cut the diameters in half to get radii):\n\nh = 34\nr = 8.5\nR = 17\n\nV = Pi(17^2+(8.5)(17)+8.5^2) 34 / 3\nV = Pi(289 + 144.5 + 72.25) 34/3\nV = Pi(505.75)34/3\nV = Pi(505.74)(10.333)\nV = Pi(5731.833)\nV = 18007 cubic inches
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The area of the trapezoid is the average of the bases times the height.\n\nThe average of the bases (2x + 4x)/2 = 3x, which is also the height.  So:\n3x * 3x = 324\n9x² = 324\nx² = 36\nx = 6\n\nSo the bases are 12 and 24 and the height is 18.
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V = area of base times height\nheight = 14\nbase = 3*3*pi = 9pi\nV = 14*9pi\nV = 126pi\nV = 395.8
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The figure we are talking about is an isosceles trapezoid. The lower base is equal to the two diagonals and the upper base and the two sides are all equal in length.\n\nCall the trapezoid ABCD with AB being the lower base and cd bbeing the upper base. The two sides which are both equal to the upper base are BC and AD. Also notte that AB parallel to CD.\n\nThe diagonals are AC and BD. \n\nIt turns out that the two base angles are bisected by each of the diagonals.Since the base angles are equal then they are each divided into two equal angles. Call each of them angle 1. also By the parallel postulate, angle CDB and angle must also be equal to angle 1.\n\nNow for the base to be the same length as the diagonals, triangle\nABC and Triangle must both be isosceles. This will be true only if angle ADB=.twice angle 1 and angle ACB = twice angle 1.\n\nTherefore the two base angles add up to 4 angle 1s and the agles C and D are both = 3 angle ones. Thus the four vertex angles add up to 10 angle 1s. Since the total of all angles in a quadrilateral is 360 degrees, the angle 1 must 360/10 =36 degrees.\n\nThus each base angle = 2 angle 1s = 2*36 =72 degrees and each of the upper angles must be equal to 3 angle 1s =3*36=108 degrees.\n\nIn summary angle A and angle B = 72 degrees and\nangles C and D both = 108 degrees.\n\nHope this was not too confusing. It will help if you draw a picture.
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Is it isosceles (with the legs the same length)?\n\nThen you can solve using:\na² + b² = c²\n\nc² = sqrt(52)² = 52\n\nThus a² + b² = 52\n\nIf a = b, then a² = 26\na = b = sqrt(26)\n\nOtherwise, if you don't have some other information, you can't uniquely solve for the length of the legs.  The legs could have lengths from nearly 0 to nearly sqrt(52).
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you split it into 2 ,a cone and a cylinder. first u need the slanting height of the cone and you find this by pythagorus theory for triangles ie L2 = h2 + r2, so height=6(found by subtracting the 15 from 21) radius=10 (20/2)therefore L2=6x6+10x10=136 therefore L =sqr root of 136 =11.6 surface area is A=pi*r*L\npi=3.142 so 3.142*10*11.6 = 364.5sq ft now the cylinder the surface area of a cylinder is circumference × h, or 2πr × h\nso 2*3.142*10*15 =942.6 so 942.6+364.5=1307.1 sq ft to find quantity of tins 1307.1/250=5.2 so they need 6 full tins you must check the formulas and calculations as I may have made a mistake ok
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A trapezoid has 4 sides but you talk about 12 and 16 bases - I assume you mean 12 and 16-sided polygons. The question can be answered, as stated, if we assume that the sides of each polygon are the same length - if the sides are not the same length then the question can't be answered until you tell us the lengths of the sides. Polygons with sides that are the same length are called "regular polygons."\n\nAnswer:\n\n1) The area of a 12-sided regular polygon inscribed within a circle with a radius of 1 is 3\n\n2) The area of a 16-sided regular polygon inscribed within a circle with a radius of 1 is 3.0614674589207183
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1.  Area of rt triangle whose leg is 6ft and whose\n    hypotenuse is 10ft?\n\n    Area = 24 sq. ft.  \n\n  Explanation:\n\n    First we need to find the other leg's length...\n    Using Pythagorean Theorem,\n    \n    c**2=a**2+b**2 \n       \n    where c is the hypotenuse, a is one leg, and \n    b is the other leg.\n\n    So, 100 = 36 + b**2;  b**2 = 100-36 = 64; therefore b=8.\n    Now, Area = 1/2(base*height) since the base is one leg\n    (we'll say it is a) and the height is the other leg \n    (therefore we'll name it b) \n    the Area = 1/2(8*6) = 1/2(48)= 24 sq. ft.\n\n2.   The hypotenuse is approx. 4.9 meters.\n    \n  Explanation:\n     \n     Using Pythagorean Theorem: c**2=a**2+b**2 we find that\n     c**2 = (3.5)(3.5) + (3.5)(3.5)\n     c**2 = 12.25 + 12.25\n     c**2 = 24.25\n     c = sq. rt. (24.25)\n     c = 4.9244 meters\n     hypotenuse is approx. 4.9 meters.\n\n3. hypotenuse is approx. 20 inches long.\n\n  Explanation: Area = 1/2(x)**2 \n               where x is length of one leg.\n\n     x**2 = 2*Area;\n     x**2 = 2*98\n     x**2 = 196\n     x = sq. rt. (196)\n     x = 14 inches\n\n     Now, to find length of hypotenuse, we use the\n     Pythagorean Theorem:\n\n     c**2 = a**2 + b**2; since a=b this can be rewritten so\n     c**2 = 2(a)**2\n     c**2 = 2(14)**2 -- Remember 14 is the length of a leg.\n     c**2 = 2(196)\n     c**2 = 392\n     c    = sq. rt. (392)\n     c = 19.7989\n     c is approx. 20 inches long.\n\n\n4.   The researcher will climb approx. 10 meters \n     to reach the crack.\n\n   Explanation:\n      \n      Using the Pythagorean Theorem: c**2 = a**2 + b**2\n      If we set a = 24, then c**2 = (24)**2 + b**2,\n      but we also know that c + b = 36 \n      which means c = 36 - b.\n\n      So to solve for this we need to set\n      (36-b)**2 = (24)**2 + b**2\n      1296-72b + b**2 = (24)**2 + b**2\n      1296 - 72b = (24)**2\n      1296 - 72b = 576\n      -72b = 576 - 1296\n      -72b = -720\n         b = -720/-72\n         b = 10 \n\n      And now we have our 10 meters the researcher \n      must climb to reach the crack in the tree.\n\n\n6.    Approximately a 42 inch stick is the longest stick\n      that will fit in a box that is 24 in X 30 in X 18 in.\n\n  Explanation:\n\n      First use Pythagorean Theorem to find the diagonal\n      inside the rectangle of 24 in X 30 in.\n\n      c**2 = (24)**2 + (30)**2\n      c**2 = 576 + 900\n      c**2 = 1476\n      c = approx. 38.418 in. -- we will call it 38 in.\n\n      Now, use Pythagorean Theorem to find the diagonal\n      inside the "new and invisible" rectangle that is \n      38 in. X 18 in.\n\n      c**2 = (38)**2 + (18)**2\n      c**2 = 1476 + 324\n      c**2 = 1800\n      c = sq. rt. (1800)\n      c is approx. 42.43 in.  \n      \n      We will call "c" 42 inches long.
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Even if you didn't know how to do this algebraically, you could check each of the choices above and figure out the right answer. That's why multiple choice is a bad option for math questions. \n\nThat being said, here is how you would solve it.\n\nLet x be the height of the Washington Monument.  Since the Eiffel Tower is 497 feet taller, you can write the height as x + 497.\n\nNow, we are going to examine the case if each monument were 58 feet shorter.  With this scenario, we have\nHeight of Washington Monument  = x - 58\nHeight of Eiffel Tower = x + 497 – 58 = x + 439\n\nSince the new Eiffel Tower is twice the height of the new Washington Monument, you can write them as:\n2 * Washington = Eiffel\n2(x – 58) = x + 439\n\nNow, solve for x:\n2x – 116 = x + 439\nx = 555\n\nSo, we know that the height of the Washington Monument is 555 and that the height of the Eiffel Tower is 497 feet higher--or 1052.\n\nTest the answers.  \n1052 – 455 = 597 (satisfies the first condition)\n1052 – 58 = 994; 555 – 58 = 497\n497 * 2 = 994\n\nSo your heights are indeed 555 and 1052 (none of the above).
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Find the dimensions of the base:\n36 - 4 - 4 = 28\n25 - 4 - 4 = 17\n\nSo the area of the base = 28 x 17 = 476\n\nThe height = 4\n\nSo the volume = 4 x 476 = 1904
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First use the Pythagorean Theorem.\n\nThe hypotenuse is 20. One of the legs has length x. Call the length of the other leg y.\n\nx^2 + y^2 = 20^2\nx^2 + y^2 = 400\n\nNow solve for y in terms of x.\n\ny^2 = 400 - x^2\ny = sqrt(400 - x^2)\n\nNow, since the triangle is right, the two legs are the altitude (or height) and the base.\n\nA = (1/2)*b*h\nA = (1/2)*x*y\nA = (1/2)*x*sqrt(400-x^2)\n\nThere's the area in terms of x!
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how do you din the height of a trapezoid if one of the non parallel sides is straight, and the other is slanted. Which makes the two parallel sides different lengths? Also, how would you find the width of a trapezoid in this situation?\n\nIf the length of the shorter parallel side is A and the length of the longer parallel side is B and the length of the straight side is C and the length of the slanted side is D then:\n\nthe height is:\nh = C (the length of the straight side.\n\nThe width depends on where you measure the width.\n\nI am imagining that your trapezoid looks like this:\n.__\n/__|
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Start with what you know:\narea = 60 inches^2\nheight = 12 inches\n\nNeed to find base\nStart with known equation\nA = 1/2*b*h\nsolve for b = 2*A / h = 2 * 60 / 12 = 10 inches\n\nNow you know the base solve for the new height given the new area.\nArea = 60+20 = 80 inches^2\nh = 2*A / b = 2*80 / 10 = 16 inches\nso the new height is 16 inches\n\nCheck A = 1/2 * 10 * 16 = 80 inches^2