What is circumradius of equilateral triangle?

Asked by: Wilford Larkin
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The altitude, median, angle bisector, and perpendicular bisector for each side are all the same single line. These 3 lines (one for each side) are also the lines of symmetry of the triangle. ... The circumradius of an equilateral triangle is s 3 3 \frac{s\sqrt{3}}{3} 3s3 ​​.

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Accordingly, How do you find the circumradius of an equilateral triangle?

The ratio of circumradius (R) & inradius (r) in an equilateral triangle is 2:1, so R/ r = 2:1. Here r = 7 cm so R = 2r = 2×7 = 14 cm. The circumference of the circumcircle = 2∏R = 2 X 22/7 X 14 = 88 cm.

Also to know, What is the formula of circumradius of a triangle?. The formula for the circumradius of a triangle with sides of lengths a, b, and c is (abc) / sqrt((a + b + c)(b + c - a)(c + a - b)(a + b - c)), and for a regular polygon with n sides of length s, it is s / (2sin(π / n)).

In this regard, What is meant by circumradius?

more ... the "Radius" of a polygon: it is the radius of a circle that passes through all vertices (corner points) of the polygon. Regular Polygons - Properties.

What is inradius and circumradius?

Inradius The inradius( r ) of a regular triangle( ABC ) is the radius of the incircle (having center as l), which is the largest circle that will fit inside the triangle. Circumradius: The circumradius( R ) of a triangle is the radius of the circumscribed circle (having center as O) of that triangle.

44 related questions found

What is the radius of circumcircle?

The circumcircle of three collinear points is the line on which the three points lie, often referred to as a circle of infinite radius.

What is circumradius of a right triangle?

Right triangles

The hypotenuse of the triangle is the diameter of its circumcircle, and the circumcenter is its midpoint, so the circumradius is equal to half of the hypotenuse of the right triangle.

What is circumradius of a hexagon?

The circumradius is the radius of the circumference that contains all the vertices of the regular hexagon. The inradius is the radius of the biggest circle contained entirely within the hexagon.

What is the inradius of a triangle?

The inradius of a triangle is formed by first dividing each of the three angles in half by a line (refer to dotted lines in the below image). The point at which these three lines meet is the center of the incircle, and the inradius is a line drawn from the center to perpendicularly intersect a side of the triangle.

What is the area and perimeter of equilateral triangle?

How Do You Find the Perimeter and Area of an Equilateral Triangle? The area of an equilateral triangle is √3/4 times (side)2 of the equilateral triangle and the perimeter of an equilateral triangle is 3 times of a side of the equilateral triangle.

Why is the area of an equilateral triangle different?

That means, all three internal angles are equal to each other and the only value possible is 60° each. ... In an equilateral triangle, median, angle bisector and altitude for all sides are all the same and are the lines of symmetry of the equilateral triangle. The area of an equilateral triangle is √3 a2/ 4.

What is the Apothem of an equilateral triangle?

For an equilateral triangle, the apothem is equivalent to the line segment from the midpoint of a side to the triangle's center.

Is the radius the Apothem?

1. Is the apothem the same as the radius? Apothem is also a radius, but when we talk about radius, we usually refer to a circle or a sphere. However, when we talk about apothem, it can be any other polygon as well, such as the square, triangle, or hexagon.

Do triangles have a radius?

Each triangle is Isosceles. This is because two sides are equal (the sides that are a radius). ... Every side in every triangle is of length r. This is because we have 6 congruent ("equal" in every way) equilateral triangles, and because two sides of every triangle is a radius.

What is the Orthocenter of a triangle?

An orthocenter can be defined as the point of intersection of altitudes that are drawn perpendicular from the vertex to the opposite sides of a triangle.

What is a 10 sided shape?

Answer (1 of 25): A ten sided object (polyhedron) is known as a decahedron (three dimensional) while a ten sided two dimensional figure (polygon) is known as a decagon.

What's a 7 sided shape called?

In geometry, a heptagon is a seven-sided polygon or 7-gon. The heptagon is sometimes referred to as the septagon, using "sept-" (an elision of septua-, a Latin-derived numerical prefix, rather than hepta-, a Greek-derived numerical prefix; both are cognate) together with the Greek suffix "-agon" meaning angle.

Are hexagons 6 sides?

A hexagon has six straight sides and six vertices (corners). It has six angles inside it that add up to 720°.

What are the side lengths of a 30 60 90?

30°-60°-90° Triangles

The measures of the sides are x, x√3, and 2x. In a 30°−60°−90° triangle, the length of the hypotenuse is twice the length of the shorter leg, and the length of the longer leg is √3 times the length of the shorter leg.

What is the circum radius of a triangle whose sides are 7 24 and 25 respectively?

7, 24, 25 is a Pythagorean triplet. Therefore, the given triangle is a right angled triangle. In a right-angled triangle, the circum radius measures half the hypotenuse. Additional Property: The median to the hypotenuse will also be equal to half the hypotenuse and will measure the same as the circumradius.

Where does the Circumcenter of a right triangle lie?

So for a right angled triangle, the circumcenter lies at midpoint of the hypotenuse.

Is the apothem half of the height of a triangle?

For an equilateral triangle, the apothem is 1/3 of the height, so the height is 3 times 2 ft or 6 ft. The base of the equilateral triangle is the apothem times 2√3 or 2ft times 2√3 = 4√3ft.

How do you calculate apothem?

We can also use the area formula to find the apothem if we know both the area and perimeter of a polygon. This is because we can solve for a in the formula, A = (1/2)aP, by multiplying both sides by 2 and dividing by P to get 2A / P = a. Here, the apothem has a length of 4.817 units. to find the length of the apothem.