A patio shaped like a trapezoid. It has bases of 25 feet and 20 feet and a height of 14 feet. A gallon of stain will cover 200 square feet. The stain she has chosen can only be purchased in gallon containers. How many gallons of stain does Mary need to buy to stain the patio? show your work.
199109
The formula for the area of a trapezoid is A=(a+b)h/2 so yours would be 20+25+45  45*14=630 630/2= 315 and that would mean you would need 2 gallons to stain
388671
let b = the length of the base\nh = the height = 4b-5\n\nA = 1/2bh\nA = 1/2b(4b-5)\nA = 2b² - 5/2b
412046
let x be the amount of fence added to the length of the 20 foot shed. The width = 20+x and length = [160-2(20+x)]/2=60-x\nSo area = A = (20+x)(60-x)\nNow find dA/dx and set it = 0 and solve for x
49103
An acre is equivalent to approximately:\na square of side 208.71 feet (63.61 metres).
6262
V = πr2h\n1.v = 36 cubic inches = 0.15584410891073416 us galons\n\n2. v = 36 0.15584410891073416 us gallons \n\n3.v = 72 = 0.3116882178214683 us gallons
18194
You can find how many square feet the kitchen is by multiplying 18*15. This equals 270 sq. feet.  (The * means multiplication)\n\nSince each tile is one square foot, you will need 270 tiles.  Multiply the number of tiles by $18, and thats the cost to cover the floor.\n\nEquations:  \nLength * Width\n\n(Number of Tiles) * (cost per tile)
25806
Its 65 sq.ft.\nI got this answer by the formula:-\nArea of Triangle=1/2*base*height
16115
let the sides of the squares be A yards .\nnow according to the pythagoras theorem we get\n             A^2 + A^2 = 38^2\n              2(A^2) = 1444\n                A^2 = 722\n                A = square root of 722\n                A = 26.8 yards\nmeans each side of square plot is 26.8 yards
431092
If the bases are in the ratio of k:1, then we can say they have lengths of kx and x (kx and x have ratio k:1). Let's say the trapezoid has height h.\n\nThe mid-segment of the trapezoid cuts the trapezoid into two similar trapezoids, and has length (1/2)(kx + x)\n\nThe area of a trapezoid is (1/2)(height)(b1 + b2).\n\nThe top trapezoid has height h/2, and bases kx and (1/2)(kx + x).  It has an area \nA1 = (1/2)(h/2)(kx + (1/2)(kx + x))\n     = (h/4)(kx + kx/2 + x/2)\n     = (h/4)(3kx/2 + x/2)\n     = (hx/8)(3k + 1)\n\nThe bottom trapezoid has height h/2 and bases (1/2)(kx + x) and x.  It has an area\nA2 = (1/2)(h/2)((1/2)(kx + x) + x)\n     = (h/4)(kx/2 + x/2 + x)\n     = (h/4)(kx/2 + 3x/2)\n     = (hx/8)(k + 3)\n\nIf A1:A2 = 5:2, then \n[(hx/8)(3k + 1)]/[(hx/8)(k + 3)] = 5/2\n(3k+1)/(k+3) = 5/2\n2(3k+1) = 5(k+3)\n6k + 2 = 5k + 15\nk = 13\n(C)
58722
You all thought way too hard on this one. There is no way to know who has more because the asker did not tell what size the containers were. \nWhoever had the biggest container had more because the numbers he gave are more than 1, you can not fill a container 1 and 2/3 of the way, nor can you fill one 7/4 of the way. Once they get to the top, they are full at 1 each. For example, if you try to pour 1 and 3/4 gallons (which is 7/4) into a one gallon container, you will only have one gallon in the container.\nIf both containers were the same size they both have the same amount.
435033
Think of the bottom of box B. It's 3ft by 3ft. So you could fit 4 of box A in the bottom layer because 2 box As are three feet wide. Then you could fit 4 more in the next layer, because box B is 3 feet high, and two box As are 3 feet high. So its a total of 8.
156919
If the tank is a cylinder, the Volume is πr²h.  If you get the volume in cubic feet, multiply by 7.5 to get gallons.
46435
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
488814
1 sq. ft = 12 inches x 12 inches = 144 sq. inches x 2.54 cm/inch x 2.54 cm/inch = 929 sq. cm. / sq. ft.\n\n1500 sq. ft * 929 sq. cm / sq. ft = 1,393,545.6 sq. cm.\n\nA sugar cube is 1.2 cm x 1.2 cm = 1.44 sq. cm.\n\nDivide the two to figure the number of sugar cubes:\n1,393,545.6 / 1.44\n\nYou can fit 967,740 sugar cubes on the floor of a 1500 sq. ft house.\n\nThis is much less than Avogadro's number which is 6.0221415 x 10^23.
480778
Tape measurements will give you cubic feet and there are about 7.5 gallons of water per cubic foot.\n\nI thought I'd add an example.  If the tub is 3' wide and 2 1/2 ' deep and 5' long, its volume is 3 x 2.5 x 5, or 37.5 cu ft.  You asked for the liquid volume, so I assumed you wanted it in gallons.\n\nTo get the gallons equivalent to 37.5 cu ft, multiply by 7.5 to get 281 gallons.  It looks surprising, but it's true.
13832
Draw a rectangle to represent the lot. Lable the long side 240 and the short side 180.\nNow draw a smaller rectangle inside it so that it is the same distance from the large rectangle.\nLabel the distance between them (the lawn) as x.\n\nYou know the area of the small rectangle is its height times its width. If the height of the large rectangle is 180, then the height of the small rectangle will be 180 minus two strips of lawn or (180 - 2x). The width of the small rectangle will be 240 minus two strips of lawn or (240 - 2x).\nThe area of the small rectangle will be Width x Height or (180-2x)(240-2x).\n\nSince the area of the lawn is equal to the area of the factory, the area of the factory has to be half the area of the whole lot or 1/2x180x240 = 21600, so\n\n(180-2x)(240-2x) = 21600\n\nFactor out some 2's to make the number smaller and we have\n2(90-x)2(120-x) = 21600\n(90-x)(120-x) = 5400\nor\nx^2 - 210x + 10800 - 5400 = 0\nx^2 - 210x + 5400 = 0\nfacto\n(x-180)(x-30) = 0 solutions 180 and 30.\nSince 180 is not a viable solution the only possible one is 30.
489099
Let L be the length\nLet W be the width\nWe know the perimeter is:\n2(L + W) = 300\nSolving for L:\nL + W = 150\nL = 150 - W\n\nNow write a formula for the area:\nArea = L * W\nArea = (150 - W) * W\nArea = -W² + 150W\n\nYou can see this is the formula for a parabola.  I'll simplify things by expressing it in terms of x:\nf(x) = -x² + 150x\n\nBut it isn't in vertex form:\nf(x) = a(x - h) + k\n\nTo get it in that form, first pull out the -1 to get x²:\nf(x) = -1(x² - 150x)\n\nNow take the coefficient on the x term (-150), take half of it (-75) and square it (5625). Add and subtract this:\nf(x) = -1(x² - 150x + 5625 - 5625)\nNow you can write this as a square:\nf(x) = -1[ (x - 75)(x - 75) - 5625)\nSimplify:\nf(x) = -1(x - 75)² + 5625\n\nYou have a downward facing parabola, with a maximum vertex at the point (h, k) or (75, 5625)\n\nSo the maximum is when the width is 75. When you solve for length you get that the length is also 75. So the maximum area for the patio is a square with sides of length 75 feet.  The total area will be 5,625 sq. feet, a maximum.