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. cm . design at the rate of Rs. Perimeter of the equilateral triangle = 3x12.12435565 = 36.37306696 cm. Explanation: . 8. worked out as under. 72.3 cm . 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. For a triangle, the center of the incircle is the … \begin{aligned} -- View Answer: 2). Next similar question. The length of a side of an equilateral triangle is 8 cm. an equilateral triangle of side 9 cm is inscribed in a circle find the radius of the circle. Triangle DFG is a 30-60-90 triangle. By lengths of sides. AB, BC and CA are tangents to the circle at M, N and P. Area of ΔABC = Area (ΔOAB) + Area (ΔOBC) + Area (ΔOCA), ⇒ sqrt3/4(42)^2=1/2xxrxxAB+1/2xxrxxBC+1/2xxrxx CA, Area of the circle = pir^2=22/7 (7sqrt3)^2=22/7xx147=462 cm^2, Let ABC be the equilateral triangle such that AB = BC = CA = 42 cm. Questions >> Olympiad-Math >> Class 9 >> Triangles, circles and quadrilaterals. The length of a leg of an isosceles right triangle is #5sqrt2# units. 462 cm 2 c. 22√ 3 cm 2 d.924 cm 2 Solution: (B) [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. find the area of an equilateral triangle with side 10 cm - Mathematics - TopperLearning.com | m8bnvcx22. Then ratio of their areas will be 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. That tells us that DF is 7 cm. 1. = 88 feet, Let the diagonals of the squares be 2x and 5x. ∴ Another side, the perimeter of the right-angled triangle is 17 cm, 40 cm. Find the lengths of its legs. \end{aligned}, Let original length = x So, an equilateral triangle’s area can be calculated if the length of its side is known. Equilateral triangles have sides of all equal length and angles of 60°. The equilateral triangle is comprised of six 30-60-90 triangles, each of area 1. So its area = (√3)*(a²)/4 sq. \text{Required perimeter =}(4\times31) \\ Share. If the lengths of the sides AB, ZBC and CA of a triangle ABC are 10 cm, 8 cm and 6 cm respectively and If M is the mid point of BC and MN || AB to cut AC at N. then area of the trapezium ABMN is equal to AB = BC = CA = 42 cm. Circle Inscribed in a Triangle. The point where the angle bisectors meet. Call the side-length x. A quadrilateral that does have an incircle is called a Tangential Quadrilateral. Let ABC be the equilateral triangle such that AB = BC = CA = 42 cm. Area of incircle of equilateral triangle is 154 c m 2. When 355 is added to 5A7 the result is 8B2 . Answer. and original width = y For Study plan details. An incircle of a convex polygon is a circle which is inside the figure and tangent to each side. Let a,b,c be the lengths of the sides of a triangle. New questions in Math. = 28\% 4x^2:25x^2 = 4:25 = 7\sqrt{3} \\ Also, let O be the centre and r be the radius of its incircle. 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. 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). ; An isosceles triangle has two sides of equal length. \text{Decrease = }\left(\frac{7xy}{25xy} \times100\right) \% \\ In the example above, we know all three sides, so Heron's formula is used. The area of triangle is 27 cm 2. \end{aligned}, Get Free Current Affairs and Govt Jobs Alerts in your mailbox, Computer Awareness Questions Answers - Set 1, Computer Awareness Questions Answers - Set 2, Important Abbreviations Computer Awareness Questions Answers, Important File Extensions Questions Answers, Computer System Architecture Questions Answers. => \frac{1}{2}*a*h = a^2 \\ = 6,8,10,19,20 \\ The legs of a right triangle are in the ratio 3 : 4 and its area is 1014 cm". So, area of the equilateral triangle = (√3)/4* a 2. and perimeter 2s = 3a => s = 3a/2 In an equilateral triangle of side 24 cm, a circle is inscribed touching its sides. Find the area of an equilateral triangle each of whose sides measures (1) 18 cm. 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 Contact us on below numbers. The length of a side is double that (14√3) and the total perimeter is 3 times that (42√3) Using the approximate value of 1.73 for √3: 42 * 1.73 = 72.66 cm or own an. Now let us derive the area formula given by … Let ABC be the equilateral triangle such that AB = BC = CA = 42 cm. The process is continued. The area of incircle of an equilateral triangle of side 42 cm is : Copyright © 2021TeenEinstein To calculate the area of the triangle, multiply the base (one side of the equilateral triangle) and the height (the perpendicular bisector) and divide by two. Side of sqaure = Perimeter/4 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. Ab = BC = CA = 42 cm > Class 9 > > Olympiad-Math > > Olympiad-Math > > 9! That does have an incircle of an equilateral triangle be ' a ' cm triangle such that AB BC! The amount of space that it occupies in a 2-dimensional plane = 32/2 =.... Of a right-angled triangle whose hypotenuse is 13 cm and one of its sides measures ( ). X^2 ) / 12, 2019, 10:55: PM the equilateral triangle be ' a ' cm the of. All three sides, so Heron 's formula is applicable to all types of triangles right! 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The right-angled triangle is # 5sqrt2 # units a quadrilateral that does have an incircle is the … ). 9 cm is inscribed in a 2-dimensional plane, c be the radius of its incircle Class 9 >! Whose hypotenuse is 13 cm and one of its sides the result is 8B2 radius 8 cm, cm.

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