Question 12. So the area of the park will be 154cm 2. The area of incircle of an equilateral triangle is 154 cm2 . The incircle is then a third of this because the incentre is the centroid, and the centre of gravity is a third of the way up the median, so in-radius R is x / 2 sqrt(3). Now using the properties of a 30, 60, 90, I can get the length of half of one side of the triangle, just multiply by sqrt(3). Given that, area of a circle inscribed in an equilateral triangle = 154 c m 2 Therefore, π (a 2 3) 2 = 154 We have to find the perimeter of the triangle. Show transcribed image text. [15] The ratio of the area of the incircle to the area of an equilateral triangle, π 3 3 {\displaystyle {\frac {\pi … The center of the incircle, called the incenter, can be found as the intersection of the three internal angle bisectors. Find the perimeter of the triangle. Help us out by expanding it.. An incircle of a convex polygon is a circle which is inside the figure and tangent to each side. To ask Unlimited Maths doubts download Doubtnut from - https://goo.gl/9WZjCW The area of a circle inscribed in an equilateral triangle is `154 cm^2`. #color(white)("XXX")s=2t = 7*sqrt(3)#, #color(white)("XXXx")=12.11# (since we are told to use #sqrt(3)=1.73#), #color(white)("XXXXXX")=3 xx 12.11 = 36.33#, 5614 views The length of a leg of an isosceles right triangle is #5sqrt2# units. Below image shows an equilateral triangle with incircle: Approach: Area of circle = and perimeter of circle = , where r is the radius of given circle. Substitute x = 21 to get 147 (pi) / 4 as your answer. (22/7) × r 2 = 154. The perimeter of the triangle is . Area of incircle of an equilateral triangle = 154 cm². The area of incircle of an equilateral triangle is 154 cm 2. Math. So half of one side of the triangle is sqrt(154*3/pi). Can you explain this answer? What is the perimeter of the triangle? From an interior point P of an equilateral triangle ABC draw lines perpendicular to the sides. 3S + A r = A R. In the equilateral triangle R = 2r. Find the perimeter of the triangle. 71.5 cm . #color(white)("XXX")pi = 22/7#, #rArr r= 7# (after some minor arithmetic), If #s# is the length of one side of the equilateral triangle and #t# is half of #s#, and The triangle of largest area of all those inscribed in a given circle is equilateral; and the triangle of smallest area of all those circumscribed around a given circle is equilateral. Find the perimeter of the triangle. Area of the circle = 154 cm 2. The Inradius of an Incircle of an equilateral triangle can be calculated using the formula: , where is the length of the side of equilateral triangle. Every triangle and regular polygon has a unique incircle, but in general polygons with 4 or more sides (such as non-square rectangles) do not have an incircle.A quadrilateral that does have an incircle is called a Tangential Quadrilateral. | EduRev CAT Question is disucussed on EduRev Study Group by 165 CAT Students. The square of the radius of the incircle is the square of the length of the shortest side of these triangles which derives from the area of one smaller triangle: ½r²√3 = 1. Question: Question5 Not Yet Answered Points Out Of 1.00 An Equilateral Triangle Has An Incircle Of Radius R Figure. in case of equilateral triangle, however, the ratio r/R can be found and is =1/2. We know that, the radius of a circle inscribed in a equilateral triangle = a 2 3 Where, a be the length of the side of an equilatral triangle. 72.3 cm . A triangle is a polygon with three edges and three vertices.It is one of the basic shapes in geometry.A triangle with vertices A, B, and C is denoted .. 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