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How do you find the area of a hexagon when given the apothem?
Apothem is the line segment that is drawn from the center and is perpendicular to the side of the hexagon. We can find the area of a regular hexagon with apothem using the formula, Area of hexagon = (1/2) × a × P; where ‘a’ is the apothem and ‘P’ is the perimeter of the hexagon.
What is the area of a regular hexagon with an apothem of 6?
summary: The area of a regular hexagon with an apothem of 6m length is 72√3 square meters.
How do you find the area of a shape with the apothem?
You also learned the formula for finding the area of any regular polygon if you know the length of one side and the apothem: A = (n × s × a)2 A = ( n × s × a ) 2 , where n is the number of sides, s is the length of one side, and a is the apothem.
How do you find the side length of a hexagon with just the apothem?
To do this, use a calculator or a trigonometry table. Multiply the tangent by 2, then divide the side length by this number. This will give you the length of the apothem of your hexagon. So, the apothem of a regular hexagon with 8-cm sides is about 6.93 cm.
What is apothem in triangle?
The apothem (sometimes abbreviated as apo) of a regular polygon is a line segment from the center to the midpoint of one of its sides. Equivalently, it is the line drawn from the center of the polygon that is perpendicular to one of its sides.
What is apothem of hexagon?
The apothem of a hexagon is the length of the line that joins the center of the hexagon with the center of one side. The apothem is the perpendicular line that connects the center of the hexagon with one side.
Is the apothem of a hexagon equal to the side length?
For the regular triangle, all sides are of the same length, which is the length of the side of the hexagon they form. We will call this a . And the height of a triangle will be h = √3/2 * a , which is the exact value of the apothem in this case.
How do you find the area of a pentagon with only the apothem?
If the apothem of the regular pentagon is given, then its area can be calculated using the formula: Area of pentagon = 1/2 × p × a; where ‘p’ is the perimeter of the pentagon and ‘a’ is the apothem.
How do you find the area of the side of a hexagon?
The simplest, and by far most common, way of finding the length of a regular hexagon’s sides is using the following formula: s = P ÷ 6, where P is the perimeter of the hexagon, and s is the length of any one of its sides.
How do you find area of a hexagon?
Since a regular hexagon is comprised of six equilateral triangles, the formula for finding the area of a hexagon is derived from the formula of finding the area of an equilateral triangle. The formula for finding the area of a hexagon is Area = (3√3 s2)/ 2 where s is the length of a side of the regular hexagon.
Is the apothem half the height of a triangle?
Note that the apothem of the triangle (labeled in Figure 11 as r1) is now equal to 1/3 the height. The centroid of an equilateral triangle is the intersection of the medians of the triangle . The median of an equilateral triangle is congruent to the apothem. .
What is the apothem of a hexagon with a side of 8?
So, the apothem of a regular hexagon with 8-cm sides is about 6.93 cm.
What is the area of the hexagon with an apothem of 3.5 units?
The side is 1/2 of 7 = 3.5. The area of a regular hexagon is (3√3 *3.5^2)/2 =31.82 or 32 cm, approximately.
What is the area of a hexagon using apothem?
In such a case, the area of the hexagon is: The apothem, a, of a regular hexagon is half of the distance between opposite sides of the hexagon. The area formula using the apothem is: Finding area using a grid
How do you find the area of a hexagon with 6 triangles?
If you know that the hexagon is missing exactly one triangle, you can also just find the area of the hexagon by multiplying the total area by 5/6, since the hexagon is retaining the area of 5 of its 6 triangles. If it’s missing two triangles, you can multiply the total area by 4/6 (2/3), and so on.
How do you find the area of a polygon with apothem?
Just plug in the length of one of the sides and then solve the formula to find the area. If you don’t have one of the side lengths but you do have the apothem, you can use the formula a = 1/2 × perimeter × apothem, where a is the area.
What is the apothem of a triangle?
Just as a reminder, the apothem is the distance between the midpoint of any of the sides and the center. It can be viewed as the height of the equilateral triangle formed taking one side and two radii of the hexagon (each of the colored areas in the image above).