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Click below to see ALL problems on Surface-areaQuestion 203384: what is the area that an it is provided triangle whose apothem is 8 yards? price by Theo(11679) (Show Source): You have the right to put this equipment on your website! to obtain the apothemn, friend inscribe a circle inside the it is intended triangle.-----the radius of that circle will certainly intersect every side exactly in the middle and will be perpendicular to each side at that point.-----if you attract a line from the center of that circle to every of the corners the the triange, climate the facility of that circle divides the equilateral triangle into 3 separate triangles. Each one of those separate triangles has a next of the equilateral triangle together it"s base and also the lines attracted from the facility of the circle come each corner of the triangle together it"s other two sides. -----each one of those triangles has a 120 degree angle at the center of the circle and two 30 level angles at every end.-----the apothem in every in each of those 3 separate triangles is the perpendicular bisector each of them.-----what you have actually is 6 separate appropriate triangles developed from those 3 separate triangles that have one edge of 60 degrees, one edge of 90 degrees, and also one angle of 30 levels each.-----since the apothem is the elevation of each of those 6 ideal triangles, climate the base of each of those 6 best triangles is equal to the apothem of each of those ideal triangles * cot(30) whereby 30 to represent 30 degrees.-----this is derivede as follows:-----cot 30) = nearby side / opposite side = basic / apothem.-----cot(30) = 1/tan(30) = 1/.577350269 = 1.732050808-----cot(30) = basic / apothem = base/8 where 8 is the length of the apothem.-----multiply both political parties of this equation through 8 come get:base the each right triangle = cot(30) * 8 = 1.732050808 * 8 = 13.85640646-----since base of each ideal triangle = 1/2 the size of every side of the equilateral triangle, climate each side of the equilateral triangle equates to 2 * 13.85640646 = 27.71281292-----the area that the it is intended triangle should be able to be acquired in a couple of ways.-----one method is to gain the area of each of the best triangles and multiply by 6.area that each ideal triangle is 1/2 * 8 * 13.85640646 = 55.42562584 * 6 = 332.5537551-----another method is to usage the formula because that the area the an it is provided triangle i beg your pardon is which becomes .-----we get the very same answer both ways which is a good sign.-----the apothem is 8 (given).each side of the equiateral triangle is 27.71281292 yards long.-----your prize is:area that the equilateral triangle is 332.5537551 square yards.-----to attract your very own picture, carry out the following.-----equilateral triangle = ABCD = center of enrolled circle.DE is perpendicular bisector the BCDF is perpendicular bisector that ACDG is perpendicular bisector the ABDraw DB, DC, DA-----your 3 separate triangles are:BDC, BDA, ADC-----your 6 separate right triangles are:BDE, CDE (from BDC)BDG, ADG (from BDA)CDF, ADF (from ADC)-----your apothems are:DE, DF, DG-----if you need a picture, permit me know and also i"ll occupational one up and also send it to you. Try drawing your very own first.-----