an equilateral triangle of side 9 cm is inscribed in a circle find the radius of the circle. Let the side length of the equilateral triangle = x Area of incircle = (1/12) πx² Area of circumcircle = (1/3) πx² so ratio circumcircle area / incircle area = (1/3) / (1/12) ... [b/c the πx² bits cancel] = (1/3) * (12/1) = 4/1 so area circumcircle : area incircle = 4 : 1 skv94573 skv94573 1/4. \text{Area of incircle =} \\ The radius, r, of the incircle of an equilateral triangle is 1/3 of its height, h, which, in turn, is s*sqrt(3)/2 (by the Pythagorean Theorem), where s is the side of the triangle. Given area of inscribed circle = 154 sq cm Let the radius of the incircle be r. ⇒ Area of this circle = πr 2 = 154 (22/7) × r 2 = 154 ⇒ r 2 = 154 × (7/22) = 49 ∴ r = 7 cm Recall that incentre of a circle is the point of intersection of the angular bisectors. This formula is applicable to all types of triangles. Area of the circle = 462 sq cm = (22/7)*r^2 r^2 = 462*7/22 = 147, or r = 12.12435565 cm Each side of the equilateral triangle = 2*12.12435565 cos 60 = 12.12435565 cm. Its perimeter 2s = 3a; ==> s = 3a/2. Solution: Given, a = 10 cm. 0.35 per cm 2. Find the area of an equilateral triangle each of whose sides measures (1) 18 cm. Let a/2 = half the length of side of the equilateral triangle => (a/2) / r = cot30° => a/2 = 8√3 cm An equilateral triangle of side 9 cm is inscribed in a circle find the radius - 1259681 anjali82 anjali82 26.06.2017 Math Secondary School An equilateral triangle of side 9 cm is inscribed in a circle find the radius 2 See answers mysticd mysticd Answer: Step-by-step explanation: ∆ABC is an equilateral triangle. Chat with tutors. All of that over 4. [16] : An excircle or escribed circle of the triangle is a circle lying outside the triangle, tangent to one of its sides and tangent to the extensions of the other two.Every triangle has three distinct excircles, each tangent to one of the triangle's sides. The area of the region lying between the circumcircle and the incircle of the triangle is (use: π =22/7) (a) 50 1 7 cm 2 (b) 50 2 7 cm 2 (c) 75 1 7 cm 2 (d) 75 2 7 cm 2 Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM The area of a circle inscribed in an equilateral triangle is 154cm 2. Example 1: If you are given altitude h and you want to calculate side a, then you need to use formula which connects h and a.. Then ratio of their areas will be The area of the remaining portion of the triangle is (\(\sqrt{3}\) =1.732) \frac{1}{2}*{2x}^2:\frac{1}{2}*{5x}^2 \\ = [6^2+8^2+10^2+19^2+20^2] \\ New questions in Math. KiLength of medians = L, 1/2 of the side =24/2=12 So, 24^2=12^2+L^2 Or, L^2=24^2–12^2=(24+12)(24–12) =36×12=6^2×2^2×(√3)^2 L=6×2×√3=12×1.732 =20.784 cm 2/3 of median =(2/3)(20.784) =13.856 cm= radius of inscribed circle. The area of incircle of an equilateral triangle is 154 cm 2. By heron’s formula, we know; A = √[s(s-a)(s-b)(s-c)] Hence, A = √[16(16-4)(16-13)(16-15)] = √(16 x 12 x 3 x 1) = √576 = 24 sq.cm. Perimeter of the equilateral triangle = 3x12.12435565 = 36.37306696 cm. 9. Inradius: The radius of the incircle. An equilateral triangle of side 9 cm is inscribed in a circle find the radius - 1259681 anjali82 anjali82 26.06.2017 Math ... Find The area of triangle base-5cm, height-4cm Give answer in photo Find the measure of the angle θ rounded to the nearest whole degree. The radius is given by the formula: where: a is the area of the triangle. Also, let O be the centre and r be the radius of its incircle. find the area of an equilateral triangle with side 10 cm - Mathematics - TopperLearning.com | m8bnvcx22. In the figure shown the height BH measures √3m. The length of a side of an equilateral triangle is 8 cm. Questions >> Olympiad-Math >> Class 9 >> Triangles, circles and quadrilaterals. cm. The process is continued. Solution : Let the side of the equilateral triangle is a . what is the largest possible value of A cot … The center of the incircle, called the incenter, can be found as the intersection of the three internal angle bisectors. \text{Decrease = }\left(\frac{7xy}{25xy} \times100\right) \% \\ Need assistance? (take =1.732) OR. Also, let O be the centre and, 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. 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. Equilateral triangles have sides of all equal length and angles of 60°. 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. The area of triangle is 27 cm 2. \end{aligned}, Let original length = x If you had an equilateral triangle where each of the sides were 2, then this would be 2 squared over 4, which is just 1. Find the perimeter of the triangle. Email . figure. Area of triangle = (s(s a)(s b)(s c)) Here, s is the semi-perimeter, and a, b, c are the sides of the triangle Given a = 18 cm, b = 10 cm and Perimeter = 42 cm Semi-Perimeter = s So its area = (√3)*(a²)/4 sq. Let ABC be the equilateral triangle such that AB = BC = CA = 42 cm. The internal angles of the equilateral triangle are also the same, that is, 60 degrees. We present a series of equilateral triangle problems, solved step by step, where you will be able to appreciate how these types of triangle problems are solved. A new equilateral triangle is formed by joining the mid-points of one, then a third equilateral triangle is formed by joining the mid-points of second. Side of sqaure = Perimeter/4 (a) 18 cm (b) 16 m (c) 14 cm (d) 12 cm Q66. \frac{22}{7}*49*3 = 462 cm^2 Login. 15. By lengths of sides. You have answered:0/50. Answer. 71.5 cm . Correct Option is : 4. Triangles can be classified according to the lengths of their sides: An equilateral triangle has three sides of the same length. -- View Answer: 2). Example: A triangle PQR has sides 4 cm, 13 cm and 15 cm. The area of the incircle of an equilateral triangle of side 42 cm is. GD is perpendicular to BC. The area of the remaining portion of the triangle is (\(\sqrt{3}\) =1.732) A) 98.55 sq. Given here is an equilateral triangle with side length a, the task is to find the area of the circle inscribed in that equilateral triangle. The location of the center of the incircle. In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. Answer. Click hereto get an answer to your question ️ In fig., an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Also, let O be the centre and r be the radius of its incircle. For Study plan details. = xy-\left( \frac{80x}{100}\times\frac{90y}{100}\right) \\ 5). So we will use area to get, Area of incircle= 154. π r 2 = 154. r = 154 π c m. Decrease in area will be Can you explain which equation you used to find the area how did you obtain root 3 /4 sry ishitha0000001 ishitha0000001 hope this will help you . The perimeter of the triangle is (a) 71.5 cm Of all the triangles drawn for the incircle with radius 8 cm, the equilateral triangle will have the least area. Triangle DFG is a 30-60-90 triangle. => Breadth = 34 feet Find the area of the triangle. On a circular table cover of radius 42 cm, a design is formed by a girl leaving an equilateral triangle ABC in the middle, as shown in the figure. ... Area: Altitudes of sides a and c: Altitude of side b: Median of sides a and c: design at the rate of Rs. One side of a right-angled triangular scarf is 80 cm and its longest side is 1 m. Find its cost at the rate of * 250 per mº. Find the perimeter of the triangle. The sides are in the ratio of 1:2:√3 for DF:DG:FG. Examples: Input : a = 4 Output : 4.1887902047863905 Input : a = 10 Output : 26.1799387799 \left(\frac{24}{4}\right),\left(\frac{32}{4}\right),\left(\frac{40}{4}\right),\left(\frac{76}{4}\right),\left(\frac{80}{4}\right) \\ Education Franchise × Contact Us. And the denominator, we have a 2 times a 2. \begin{aligned} \text{Radius of incircle} = \frac{a}{2\sqrt3} \\ = \frac{42}{2\sqrt3} \\ = 7\sqrt{3} \\ \text{Area of incircle =} \\ \frac{22}{7}*49*3 = 462 cm^2 \end{aligned} \end{aligned}, We are given with length and area, so we can find the breadth. An incircle of a convex polygon is a circle which is inside the figure and tangent to each side. Ask Questions, Get Answers Menu X. home ask tuition questions practice papers mobile tutors pricing. Share. worked out as under. [15] The ratio of the area of the incircle to the area of an equilateral triangle, π 3 3 {\displaystyle {\frac {\pi }{3{\sqrt {3}}}}} , is larger than that of any non-equilateral triangle. Next similar question. touching its sides. ∴ Another side, the perimeter of the right-angled triangle is 17 cm, 40 cm. The area of an equilateral triangle which side 2 root 3 cm 2 See answers ... Area of an equilateral triangle . 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). = \left(xy- \frac{18}{25}xy\right) \\ X . = 124 cm Academic Partner. The area of the incircle of an equilateral triangle of side 42 cm is : (a) 22 73 cm² (b) 231 cm² (c) 462 cm² (d) 924 cm² Solution: Side of an equilateral triangle (a) = 42 cm Radius of inscribed circle = \(\frac { 1 }{ 3 }\) x altitude. \begin{aligned} The area is given by: where p is half the perimeter, or 72.3 cm . Area of bigger circle = πr 2 = 1386 cm 2 ⇒ × r 2 = 1386 ⇒ r = 21 cm ⇒ GF = 2r = 42 cm Since the bigger circle is incircle of ABC, GF = AF ⇒ AF = 63 cm AG = AF – GF = 63 – 42 = 21 cm Now in ADE, the smaller circle is incircle Radius of smaller circle = AG = 7 cm Area of smaller circle = × 7 × 7 = 154 cm 2 \text{Area of new square will be }\\ Find the area of a right-angled triangle whose hypotenuse is 13 cm and one of its sides containing the right angle is 12 cm. Then apply Pythagoras to get the altitude of the triangle is x sqrt(3)/2. The perimeter of the triangle is . In an equilateral triangle of side 24 cm, a circle is inscribed. \begin{aligned} \text{Radius of incircle} = \frac{a}{2\sqrt3} \\ AB = BC = CA = 42 cm. Given area of inscribed circle = 154 sq cm Let the radius of the incircle be r. ⇒ Area of this circle = πr 2 = 154 (22/7) × r 2 = 154 ⇒ r 2 = 154 × (7/22) = 49 ∴ r = 7 cm Recall that incentre of a circle is the point of intersection of the angular bisectors. Find the covered area of the design. ∴ Area of Equilateral Triangle = a²√3/4 Problems Solving. AB, BC and CA are tangents to the circle at M, N and P. ∴ O M = O N = O P = r. Area of ΔABC = Area (ΔOAB) + Area (ΔOBC) + Area (ΔOCA) ⇒ … The area of an equilateral triangle is the amount of space that it occupies in a 2-dimensional plane. = \frac{7}{25}xy \\ Geometry calculator for solving the circumscribed circle radius of an equilateral triangle given the length of a side ... Equilateral Triangle: All three sides have equal length All three angles are equal to 60 degrees. Expert Answer: Let triangle ABC be an equilateral triangle of side 9 cm and AD is the median where G be the centroid of the triangle which divides median into 2:1. Let a,b,c be the lengths of the sides of a triangle. Answer. To recall, an equilateral triangle is a triangle in which all the sides are equal and the measure of all the internal angles is 60°. We have to find the perimeter of the triangle. Since DF is 7, FG will be 7√3. = 28\% Click here to get an answer to your question ️ The area of incircle of an equilateral triangle of side 42 cm is by brainly Ankush2802 Ankush2802 07.11.2018 8. What will be the ratio between the area of a rectangle and the area of a triangle with one of the sides of the rectangle as base and a vertex on the opposite side of the rectangle ? Given ABC is an equilateral triangle … cm . = \frac{42}{2\sqrt3} \\ Contact us on below numbers. Then apply Pythagoras to get the altitude of the triangle is x sqrt(3)/2. In right triangle ADB, AD 2 + DB 2 = AB 2 where AB … Problem 01. A quadrilateral that does have an incircle is called a Tangential Quadrilateral. = 6,8,10,19,20 \\ (1) 20 cm [Take V3 =1.73) Asked by atyagi.salesforce | 14th Oct, 2019, 10:55: PM. = 36+64+100+361+400 \\ Question 9: The area of the incircle of an equilateral triangle of side 42 cm is a. Find the lengths of its legs. Let a be the length of the sides, A - the area of the triangle, p the perimeter, R - the radius of the circumscribed circle, r - the radius of the inscribed circle, h - the altitude (height) from any side.. \begin{aligned} To find the height, we can draw an altitude to one of the sides in order to split the triangle into two equal 30-60-90 triangles. 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). cm 231 cm 2 b. Perimeter of the equilateral triangle = 3x12.12435565 = 36.37306696 cm. O is the incentre of the equilateral ΔABC. The point where the angle bisectors meet. So sides are, \begin{aligned} Minimum area of a triangle in which a incircle with radius 8 cm can be drawn = 192√3 sq. \end{aligned}, \begin{aligned} For a triangle, the center of the incircle is the … \text{We know area of square =}a^2 \\ 8B2 is divisible by 3 . 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