Geometry calculator for solving the circumscribed circle radius of an equilateral triangle given the length of a side By the formula : . Three kinds of cevians are equal for (and only for) equilateral triangles: The three altitudes have equal lengths. Enter one value and choose the number of decimal places. Examples: Input: R = 4 Output: 20.784 Explanation: Area of equilateral triangle inscribed in a circle of radius R will be 20.784, whereas side of the triangle will be 6.928 Below image shows an equilateral triangle with circumcircle: The formula used to calculate the area of circumscribed circle is: (π*a 2)/3. To recall, an equilateral triangle is a triangle whose all sides are equal and the measure of all the internal angles is 60°. Using sine ratio rule, For triangle ODC, opposite is a cm and hypotenuse is of length 8 cm . Step 3 The inscribed circle’s center of an equilateral triangle is the point of intersection of the medians. Explanation: . the radius of circle inscribed by equilateral triangle is [math]r=\frac{\text{area of triangle}}{\text{semi-perimeter of triangle}}=\frac{\Delta}{s}[/math] [math]=\frac{\frac{\sqrt3}{4}a^2}{\frac{3a}{2}}[/math] So, an equilateral triangle’s area can be calculated if the length of its side is known. The area of an equilateral triangle is the amount of space that it occupies in a 2-dimensional surface. (Sorry if my diagram does not appear to have congruent sub-triangles; they really are congruent). The area of an equilateral triangle can be calculated in the usual way, but in this special case of an equilateral triangle, it is also given by the formula: where S is the length of any one side. The circumradius of a triangle is the radius of the circle circumscribing the triangle. Equilateral triangles have sides of all equal length and angles of 60°. Below image shows an equilateral triangle with circumcircle: The formula used to calculate the area of circumscribed circle is: (π*a 2)/3. Question: A circle has a radius of 6 in. Calculations at an equilateral triangle or regular trigon. To find the area, we can first find the height. To find : Find the area . The altitude shown h is hb or, the altitude of b. In this way, the equilateral triangle is in company with the circle and the sphere whose full structures are determined by supplying only the radius. Multiplying both sides by 8. So the length of the apothem is 4 cm . In an equilateral triangle, the altitudes, the angle bisectors, the perpendicular bisectors and the medians to each side coincide. So we will get. Basic Properties Because the equilateral triangle is, in some sense, the simplest polygon, many typically important properties are easily calculable. If you have any 1 known you can find the other 4 unknowns. This is the most simple regular polygon (polygon with equal sides and angles). A triangle is circumscribed in a circle if all three vertices of the triangle are tangent to the circle.

Solution : We have given that . Given an integer R which denotes the radius of a circle, the task is to find the area of an equilateral triangle inscribed in this circle..

The three angles of an equilateral triangle are also of equal measure in Euclidean geometry. See Area of an equilateral triangle. Then click Calculate. An equilateral triangle is a special case of a triangle where all 3 sides have equal length and all 3 angles are equal to 60 degrees. 19.

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