How do you find the area of an equilateral triangle inscribed in a circle?

The area of a circle inscribed inside an equilateral triangle is found using the mathematical formula πa2/12. Lets see how this formula is derived, Formula to find the radius of the inscribed circle = area of the triangle / semi-perimeter of triangle.

What is the formula for finding area of an equilateral triangle?

In general, the height of an equilateral triangle is equal to √3 / 2 times a side of the equilateral triangle. The area of an equilateral triangle is equal to 1/2 * √3s/ 2 * s = √3s2/4.

How do you construct the center of an equilateral triangle?

In the familiar Euclidean geometry, an equilateral triangle is also equiangular; that is, all three internal angles are also congruent to each other and are each 60°….

How do you find the radius of an equilateral triangle in a circle?

For finding the radius of the circle use the formula r=(s−a)tanA2 and the known thing that s of a equilateral triangle is half of three times of its sides and all angles are equal to 60∘.

What is the formula of equilateral triangle height?

Formula to calculate height of an equilateral triangle is given as: Height of an equilateral triangle, h = (√3/2)a, where a is the side of the equilateral triangle.

How do you prove an equilateral triangle in a circle?

Let the centre of the circle be O.. Join all the points p, q, r to the center(O) of the circle. As it is given arcs arcPQ=arcQR=arcRP ,lines OP,OQ,OR divides the circle into three equal sectors,with all equal angles. therefore PQ=PR=RQ so the triangle PQR will be an equilateral triangle..

How do you find the side of an equilateral triangle?

Given: Perimeter of an equilateral triangle = 12 cm As per formula: Perimeter of the equilateral triangle = 3a, where “a” is the side of the equilateral triangle. Step 1: Find the side of an equilateral triangle using perimeter. 3a = 12

What is an equilateral triangle called?

An equilateral triangle is a triangle that has sides that are all equal in length. △ABC is an equilateral triangle since AB≅AC≅BC. An isosceles triangle has at least two equal sides, so an equilateral triangle is also an isosceles triangle. An equilateral triangle is also called an equiangular triangle since its three angles are equal to 60°.

What is the perimeter of an equilateral triangle whose area is 12 cm?

The perimeter of an equilateral triangle is 3a. Question 1: Find the area of an equilateral triangle whose perimeter is 12 cm. As per formula: Perimeter of the equilateral triangle = 3a, where “a” is the side of the equilateral triangle. Step 1: Find the side of an equilateral triangle using perimeter. Thus, the length of side is 4 cm.

How many Schläfli symbols are in a equilateral triangle?

Equilateral triangle Type Regular polygon Edges and vertices 3 Schläfli symbol {3} Coxeter diagram