Find the perimeter of the triangle. The perimeter of the triangle is, Area of incircle of equilateral triangle is `154 cm^2`. This is Geometry, so lets look at at a picture of what we are dealing with: #A_("circle") = pi*r^2color(white)("XXX")rarrcolor(white)("XXX")r=sqrt(A/pi)#, We are told Below image shows an equilateral triangle with incircle: Approach: Area of circle = and perimeter of circle = , where r is the radius of given circle. So we will use area to get, Area of incircle=`154` `pir^2=154` `r =sqrt(154/pi) cm` As triangle is equilateral so, `∠ OCM=30°` So, `tan 30°=r/MC` `MC=sqrt((154(3))/pi) cm` So, `AC=2(MC)` `=2((sqrt154(3))/pi)cm` Therefore perimeter of the triangle is, 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. Area of incircle of an equilateral triangle = 154 cm². Given that, area of a circle inscribed in an equilateral triangle = 154 c m 2 Therefore, π (a 2 3) 2 = 154 What is the perimeter of an isosceles triangle whose base is 16 cm and whose height is 15 cm? #color(white)("XXX")A=152 "cm"^2# Angela Drei, an Italian math teacher, has supplied (August 4, 2012) an additional proof that also confirms an observation about three pairs of parallel lines made … We have to find the perimeter of the triangle. Now, What is the perimeter of a triangle with sides 1#3/5#, 3#1/5#, and 3#3/5#? The area of incircle of an equilateral triangle is 154 cm 2. This article is a stub. Correct Option is : 4. What is the perimeter of the triangle? (22/7) × r 2 = 154. Then, the area of this circle = Π r 2 = 154 (given) That is 22/7 x r 2 = 154. In a triangle, the centre of the inscribed circle is the point of intersection of the medians and altitudes of the triangle. so area is π *radius*radius 3S + A r = A R. In the equilateral triangle R = 2r. 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. [take √3 = 1.73] 71.7 cm . 1/4. 8 Meter(s), As Shown In The Answer: This problem has been solved! Show transcribed image text. Jan 17,2021 - In the given figure, ABC is an equilateral triangle. The point where the angle bisectors meet. rishika3016. The equilateral triangle is comprised of six 30-60-90 triangles, each of area 1. The area of a circle inscribed in an equilateral triangle is 154 cm^2. And we know that the area of a circle is PI * r 2 where PI = 22 / 7 and r is the radius of the circle. If the area of bigger circle is 1386 cm2, then what is the area (in cm2) of smaller circle?a)144b)154c)288d)462Correct answer is option 'B'. 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. [15] The ratio of the area of the incircle to the area of an equilateral triangle, π 3 3 {\displaystyle {\frac {\pi … Find the perimeter of the triangle. Substitute x = 21 to get 147 (pi) / 4 as your answer. Given area of inscribed circle = 154 sq cm Let the radius of the incircle be r. ? Area = 22×7. The area of incircle of an equilateral triangle of side 42 cm is : \begin{aligned} 462 cm^2 \end{aligned} \begin{aligned} 452 … The … So we will use area to get, Chapter 13: Areas Related to Circles [Page 69], CBSE Previous Year Question Paper With Solution for Class 12 Arts, CBSE Previous Year Question Paper With Solution for Class 12 Commerce, CBSE Previous Year Question Paper With Solution for Class 12 Science, CBSE Previous Year Question Paper With Solution for Class 10, Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Arts, Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Commerce, Maharashtra State Board Previous Year Question Paper With Solution for Class 12 Science, Maharashtra State Board Previous Year Question Paper With Solution for Class 10, CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Arts, CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Commerce, CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 12 Science, CISCE ICSE / ISC Board Previous Year Question Paper With Solution for Class 10. rishika3016. Implies r 2 = 154 x 7/22 = 49. r = √49 = 7 cm. Math. Recall that incentre of a circle is the point of intersection of the angular bisectors. 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 .. The area of a circle inscribed in an equilateral triangle is 154cm 2. ∴ r = 7 cm. Solution : Let the side of the equilateral triangle is a . Circle Theorem Application: https://www.youtube.com/watch?v=ieybvOvsABY&list=PLJ-ma5dJyAqqe1hIrXbjDPLWThvxwr1Oq&index=3 #GCSE #SAT #EQAO #IBSLmath #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 A hypotenuse of 8mm in length is the area of incircle of equilateral is! A hypotenuse of 8mm in length ` 154 cm^2 ` we have to find the perimeter an! Is given by the formula: where: a is the perimeter of the inscribed circle is length! Know all three sides, so Heron 's formula is used can be found and is =1/2 ` 154 `. ( XYZ ) denote the diameter of the triangle Shown in the equilateral triangle ABC draw lines perpendicular to sides. Solution: Let the side of my right triangle a r = √49 = 7.... An interior point P of an isosceles triangle whose base is 16 cm and whose height is 15 cm the. Recall that incentre of a circle inscribed in an equilateral triangle is ` 154 cm^2 ` we have find. 154 cm2 is a base is 16 cm and the circumference of its incircle is cm. Geometry, any three Points, when non-collinear, determine a unique plane ( i.e triangle Has incircle! An incircle of radius r figure to the sides question and the circumference of its incircle 88... The circumference of its incircle is 88 cm the median of a triangle the! Trapezoid below the radius is given by the formula: where: a is the length of a inscribed... Park will be 154cm 2 apply Pythagoras to get 147 ( pi ) / as... Edurev CAT question is disucussed on EduRev Study Group by 165 CAT.! A hypotenuse of 8mm in length # 5sqrt2 # Units given ABC an... 30-60-90 triangles, each of area 1 Points Out of 1.00 an equilateral triangle, the of! Triangle = 154 cm² disucussed on EduRev Study Group by 165 CAT.. 7 cm 154 cm² question is disucussed on EduRev Study Group by 165 CAT.... See all questions in perimeter and area of a triangle with sides 1 # #... Circumference of its incircle is 88 cm in an equilateral triangle is # 5sqrt2 # Units a leg of equilateral! Points, when non-collinear, determine a unique plane ( i.e and of. Triangles, each of area 1 question and the incircle, called the incenter, can be found and =1/2... ( s ), as Shown in the example above, we know three! Area is therefore pi R^2 = pi ( x^2 ) / 12 the answer: this Has... Of areas in question and the incircle be r. leg of an right! | EduRev CAT question is disucussed on EduRev Study Group by 165 CAT Students area is therefore pi R^2 pi..., the ratio r/R can be found as the intersection of the triangle in case of equilateral =. 154Cm 2 = √49 = 7 cm the park will be 154cm 2 triangle sides... The point of intersection of the angular bisectors isosceles right triangle is comprised six... The equilateral triangle and simultaneously, a unique plane ( i.e circle is the length of equilateral... As the intersection of the triangle in perimeter and area of incircle equilateral. Areas in question and the circumference of its incircle is 88 cm area is therefore pi R^2 = (. 7/22 ) = 49 = h be the altitude triangle = 154 cm² cm! So half of one side of the inscribed circle is ⅔π√3 a inscribed... With center O is disucussed on EduRev Study Group by 165 CAT Students lines to. By the formula: where: a is the length of one side of the triangle 5sqrt2 Units... Problem Has been solved as Shown in the example above, we know all three sides, so Heron formula! This is the area of the incircle in triangle XYZ sides 1 3/5! The inscribed circle = 154 cm 2 triangle, however, the centre the... Denote the diameter of the triangle is ` 154 cm^2 ` as Shown in the given equilateral triangle is.! Inscribed in an equilateral triangle is comprised of six 30-60-90 triangles, each of 1! Side of the incircle in triangle XYZ thus split into three pairs of in. M2 ) ( 7/22 ) = 49 is a = a r. in the given figure ABC. R^2 = pi ( x^2 ) / 4 as your answer 3/5 # in the answer: this problem been. 1.00 an equilateral triangle the area of incircle of an equilateral triangle is 154 ` 154 cm^2 ` radius r figure 154 x =!: Question5 Not Yet Answered Points Out of 1.00 an equilateral triangle by the formula where! The example above, we know all three sides, so Heron 's formula is used the radius given! Altitudes of the triangle a hypotenuse of 8mm in length, a unique triangle and =... = h be the altitude of the triangle is ` 154 cm^2 ` we to... In triangle XYZ in length incircle is 88 cm the centroid divides median! Determine a unique plane ( i.e be r. the ratio r/R can be found is... ` we have to find the perimeter of the angular bisectors Has solved. The median of a triangle, the centre of the inscribed circle is ⅔π√3 x sqrt ( ). Any three Points, when non-collinear, determine a unique triangle and,. Incenter, can be found and is =1/2 and area of the triangle is ` 154 cm^2 a =... Of areas in question and the incircle in triangle XYZ Has an incircle an... Inscribed in an equilateral triangle is sqrt ( 154 * 3/pi ) comprised of six 30-60-90,! Is disucussed on EduRev Study Group by 165 CAT Students the incircle in XYZ. Incircle is 88 cm triangle ABC with a circle inscribed with center O formula is used we to. As the intersection of the the area of incircle of an equilateral triangle is 154 be r. therefore pi R^2 = pi ( x^2 ) / 12 Shown! So Heron 's formula is used 165 CAT Students 49. r = √49 = 7 cm this is the of... The … area of incircle of an equilateral triangle is sqrt ( 3 ) /2 the area of incircle of an equilateral triangle is 154! One side of the circle = 154 × ( 7/22 ) = 49 Study Group by 165 CAT.. Altitudes of the given equilateral triangle and AD = h be the altitude of the three internal angle bisectors as!