How do you find the area of the isoceles triangle?
199189
You can use Heron's formula if you know the length of all three sides. \nHeron's Formula:\nLet s be the semiperimeter (which is half the perimeter) and a,b,c be the length of the sides, then the area is\nA = sqrt[s*(s-a)*(s-b)*(s-c)]\nperimeter = 4+4+6 = 14\ns = 14/2 = 7 (because s is one-half the perimeter)\nA = sqrt[7(7-4)(7-4)(7-6)]\n= sqrt(7*3*3*1)\n= sqrt(63)\n= 3*sqrt(7) which is approximately 7.93725\n\nYou can also use the Pythagorean Theorem to find the height.
510642
Let x be the length for the square and 14-x for the triangle.\n\nThe area of the square is (x/4)^2 = (x^2)/16.\n\nThe height of the triangle is sqrt(3)(14-x)/6 and the base of the triangle is (14-x)/3, so the area of the triangle is\n\n1/2 bh = [(14-x)/6] [sqrt(3)(14-x)/6] = (14-x)^2 sqrt(3)/36\n\nTotal area A = (x^2)/16 + (14-x)^2 sqrt(3)/36\n\nA = [9x^2 + 4(x^2 - 28x + 196) sqrt(3)] / 144\n\nA = [(9 + 4 sqrt 3) x^2 - (112 sqrt 3) x + (784 sqrt 3)] / 144\n\ndA/dx = [2(9 + 4 sqrt 3) x - (112 sqrt 3)] / 144 = 0\n\n(9 + 4 sqrt 3) x = 56 sqrt 3\n\nx = (56 sqrt 3) / (9 + 4 sqrt 3) = 6.0895 meters  (Answer)\n\nThe area of the square is 2.32 m^2.  The area of the triangle is 3.01 m^2, and the total area is 5.33 m^2.
474394
How to find the area of an octagon:\n\nMeaning of words\n\nAn octagon is a polygon having eight sides.\nA polygon is a closed plain figure bounded by three or more straight sides that meet in pairs in the same number of vertices and do not intersect other than at these vertices.\nVertices is the plural of vertex.\nVertex means the point opposite the base of a figure or the point of intersection of two sides of a plain figure or angle.\n\nDifferent methods or formulas are used for calculating the area of polygons. The following method is used for calculating the area of an octagon.\n\nFormula: 2 × r2× 1.4142135 (the last number is the square root of 2)\n\nr = radius\n\nThe radius is a straight line from the centre to any point on the outside of the shape.\n\nFind the radius of the octagon, then perform the formula.\ne.g. if the radius of an octagon was 4 cm, then 2 × 42× 1.4142135 = 45.25 cm2, which is the area.
114451
If an object is a parallelogram, we define its area to be its length multiplied by its height. Rectangles and squares are common parallelograms.\nIf you cut a parallelogram in half along its diagonal, you get a triangle with the same width and height, but half the area. Thus the formula for the area of a triangle is (1/2)*base*height where the name "base" has replaced the now meaningless label of "length".\nUsing these two formulas, you should be able to find the area of any polygon (a closed shape with straight sides) by cutting it up into these shapes of known area. For example, a trapezoid can be cut up into a rectangle and two triangles.\nThe perimeter of a polygon is the easiest measure. Just add up the lengths of all the sides.
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Draw a picture of the triangle formed to see that the side opposite the angle is 24 and the side adjacent is k, with 25 being the hypotenuse.  Sine = opp. leg/hyp. which is 24/25\nCosine = adj. leg. / hyp. = k/25\n\nIf you need to, you can find k using the Pyhhagorean Theorem\n(k squared = 25 squared - 24 squared), keeping in mind it can be positive or negative.
530871
Just break the pentagon up into 5 triangles.  You can then add together the area of the 5 triangles to get the total area.
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The area of a triangle is 1/2 the base time the height.\n\nA=1/2bh\nA=1/2(10)(4)\nA=(5)(4)\nA=20 units^2
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go to this website and try to understand how to get the area of the shade region \n\nhttp://www.algebralab.org/lessons/lesson.aspx?file=Geometry_AreaPerCricle.xml\n\ngood luck
230835
If this is a right triangle, the formula for finding the area is 1/2 BH (base x height).  Therefore, the formula you want for this problem is 1/2[x(x-3)]=35.
102997
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
451814
Several ways. The first that comes to mind is to figure the area with Heron's formula (area = sqrt(s(s - a)(s - b)(s - c)), where s = (a + b + c)/2). The area can also be figured as 1/2 base times altitude, so you know the altitudes of the triangle. The altitudes give you right triangles where you know the hypotenuse (a side of the triangle), and a leg, so you can compute the trig functions of all the angles. Then the angles can be computed as arcsin or arccos of the angle (arcsin(altitude/side))
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180/7 °\nor 25 5/7 °\n\nSee picture:\nhttp://mudandmuck.com/str2/triangle2.JPG\n\n180-6x+2x = 3x since <A = <C (ΔABC is isoceles)\n180 = 7x\n180/7 = x
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The height of a triangle is defined as the perpendicular distance from an angle to a side.  Now, since this is a right triangle, and depending on how it is situated, the height could be 10" or 12" if you observe from the two acute angles.  But from the right angle, the height goes from the angle to AC (your hypotenuse).  Finding this one will be tricky but can be done using the Pythagorean Theorem.\n\nIf you drop a height from the right angle to the hypotenuse, it breaks it into two parts.  The length of one part is x (since we don't know and since the height doesn't perfectly bisect the hypotenuse), and the length of the other part is 15.62-x (since the total length is 15.62").  It really doesn't matter which side is x, but for my explanation, I'll use x as the side closer to the leg that is 10".  This height creates two new right triangles, and you can use the Pythagorean Theorem to find out both the height and the missing side x.\n\nOne formula will end up being 10^2 = h^2 + x^2, and the other formula will end up being 12^2 = h^2 + (15.62-x)^2.  You can solve the first equation to find that h^2 = 100 - x^2 and substitute that in to the second equation:\n\n12^2 = h^2 + (15.62-x)^2\n144 = 100 - x^2 + 243.9844 - 31.24x + x^2\n144 = 343.9844 - 31.24x\n-199.9844 = -31.24x\nx = 6.4 (rounded)\n\nKnowing this, we can find that missing height:\nh^2 = 100 - x^2\nh^2 = 100 - (6.4)^2\nh^2 = 100 - 40.98\nh^2 = 59.02\nh = 7.68"\n\nSo it all depends on the specific height you're looking for - it's either 10", 12", or 7.68".\n\nAs for your trough, surface area is the sum of all the areas.  Break your trough into parts that you can find areas of.  If you're just looking for the outer surface area, for example, you have two triangles for the ends and two rectangles for the sides (assuming that it's an open trough).  The area of the triangles is A = 0.5bh, and the area of the rectangle sides is A = bh (b in this case will be a side of the trianlge, 2, and h will be the length of the trough, 16).  So just add up all the surfaces that will comprise your trough and you should have your surface area.  (I'm not sure if you need to include the inside as well, but if so you need 2 triangles and 2 rectangles for the outside, and 2 triangles and 2 rectangles for the inside as well.)
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I wish I remembered terms for this stuff.\nFind the length of the base, divide that by two.\nUse this number to find the length of a line drawn from the point of the triangle to the base. Congrats, that number is the height.\nTriangle ABC.\nLength from point A to C is 3.\nFrom A to B is 4.\nSo B to C is 5.\nTake the base, we'll say line AC, and divide that by 2, so you get 1.5.\nUse that number, now, as the length from A to D.\nSo, 1.5 squared plus 4 squared is 18.25. Square root of 18.25 is 4.27, so your height is 4.27.\nPythagorean Theorem.\nA^2 + B^2 = C^2
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The area S of a triangle is S = ½bh, where b is the length of any side of the triangle (the base) and h (the altitude) is the perpendicular distance between the base and the vertex not on the base.
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p=72, each side=6\nyou can divide the hexagon into 6 equilateral triangles with side=6\nA of each triangle=(1/2)*6*6sqrt(3)/2=9*sqrt(3)\nfor all six, the area is 54*sqrt(3)=93.5
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In all isosceles triangles if you drop a perp. line from the apex you will automatically bisect the base.\nThis done you will have 2 similar rt. angled triangles with base of 46.75 and hypotenuse of 49.25\nThe angle opp. the perp. is found by looking up the angle whose cosine is 46.75/49.25  = 0.9492  =  18.3*\nHence, other base angle is 18.3* making base angles sum of 36.6*\nSum of the angles of a triangle is 180*\nHence, Apex angle is 180 - 36.6  =  143.4*