How do you find the area of an equilateral triangle with an apothem?
1 Expert Answer Divide 6√ 3 by 3. You now have the base of the right triangle. Multiply 2√ 3 by 2 to get the base of the equilateral triangle as well as all the sides. Use the formula of A=BH/2 to find the final area of the triangle.
What is the area of an equilateral triangle with an apothem of 6?
72√3 square meters
The apothem divides equally each one of the equilateral triangles into right triangles whose sides are the circles’ radii, apothem, and half of the hexagon’s side. Area of hexagon = 6(area of equilateral triangle). = 72√3 square meters.
What is the apothem of an equilateral triangle inscribed in a circle?
An apothem is the distance from the center of the circle to a side measured perpendicular to the side. Having the interior angles of the triangle and the radius of the circle, you should be able to calculate the length of the apothems.
What is the formula for finding the area of an equilateral triangle?
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. The perimeter of an equilateral triangle is 3a.
How do you find the apothem of a triangle?
The apothem is the distance from the center of the polygon to the midpoint of a side. In this case we have a triangle so the Apothem is the distance from the center of the triangle to the midpoint of the side of the triangle. The Apothem is perpendicular to the side of the triangle, and creates a right angle.
How do you find the area of an equilateral triangle circumscribed in a circle?
We know that area of circle = π*r2, where r is the radius of given circle. We also know that radius of Circumcircle of an equilateral triangle = (side of the equilateral triangle)/ √3. Therefore, area = π*r2 = π*a2/3.
What is apothem in triangle?
An apothem is a perpendicular segment from the center of a regular polygon to one of the sides. When radii are drawn from the center to the vertices of the polygon, congruent isosceles triangles are formed with the polygon apothem as the height. These triangles are used in calculating the area of regular polygons.
What is the formula for the area of the equilateral triangle?
What is more, we know that the sine of 60° is √3/2, so the formula for equilateral triangle area is: area = (1/2) * a² * (√3 / 2) = a² * √3 / 4 Height of the equilateral comes from sine definition: h / a = sin(60°)so h = a * sin(60°) = a * √3 / 2
What is the perimeter of an equilateral triangle whose area is 12cm?
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.
How to find the height of an equilateral triangle?
Height of the equilateral comes from sine definition: You can easily find the perimeter of an equilateral triangle by adding all triangles sides together. The regular triangle has all sides equal, so the formula for the perimeter is: How to find the radius of the circle circumscribing the three vertices and the inscribed circle radius?
How do you find the missing value of an equilateral triangle?
To calculate missing value in equilateral triangle, based on one known value, you need to remember just three formulas. F1: a = side. h = altitude. A = area. P = perimeter. F2: F3: The diagram at the right shows when to use each of these formulas.