What is a decagon?
In geometry, a decagon is a polygon with ten sides and ten angles. In a regular decagon, all sides are equal in length and all angles are 144º. The area of a regular decagon with long side a is given by: A = \ frac {5} {2} a ^ 2 \ cot \ frac {\ pi} {10} = \ frac {5a ^ 2} {2} \ sqrt {5 + 2 \ sqrt {5}} \ simeq 7,69421 a ^ 2.
How is a decagon created?
- Step # 2 – this intersects the r axis at points A and B, and the s axis at points C and D;
- Step # 3 – with radius CO, we draw an arc that intersects the circumference at points 1 and 2;
How is the area of a decagon calculated?
Calculation of the area through the side
another less similar formula that uses another approximate fixed number: Area = (Side x 1,539 / 2) x Perimeter.
How many faces does a decagon have?
A decagon is a polygon with 10 sides and 10 vertices. A regular decagon is a particular type of decagon, and it is a regular polygon with 10 sides of equal length and 10 angles of equal width equal to 144 °.
How is the hypothem of a decagon calculated?
This relationship is given by the formula a = nf xl that is apothem = fixed number for the measurement of the side. The area of a regular polygon is found by multiplying the length of the perimeter (p) by that of the apothem (a) and dividing the product by 2.
Related questions
How is apothem calculated?
The length of the apothem is calculated by multiplying the measurement of the side by the fixed number and coincides with the measurement of the height of each of the six equilateral triangles obtained by joining the vertices of the hexagon with its center.
What is apothem and how is it calculated?
In regular polygons the apothem is the radius of the circumference inscribed inside the polygon. For example, if we take a square and draw inside it a circle that has the center of the polygon as its center and the distance from the center of the polygon to the side of it as the radius. The radius is the apothem.
How many vertices does the decagon have?
Plane polygon having 10 vertices and therefore 10 sides. Of particular interest is the regular decagon, that is the convex decagon for which all sides are equal to each other and all internal angles formed by two consecutive sides are also equal to each other (they measure 144 °). The side of the decagon …
What is a 30-sided polygon called?
In geometry, the triacontagon is any polygon with 30 sides and as many vertices and angles.
How is the area of a dodecagon calculated?
For the area we can use the constant φ. A = φ L² = 11.196 10² = 1119.6 cm².
How do you find the area of the circle?
- C = 2πr, where r is the radius of the circle.
- The radius can also be expressed using the diameter so that 2r = d:
- C = πd.
- A = πr2, where r is the radius of the circle or correspondingly: A = π4d2, where d is the diameter of the circle.
- A = Cd4.
How do you calculate the area of a regular pentagon?
the area of a regular pentagon can be calculated by multiplying the square of the side measurement by the area constant φ = 1.72, or by dividing the product between the perimeter and the apothem by two, or by using one of the formulas that we will see shortly.
How do you make the decagon given the side?
We take up our compass again and, aiming at 3, with opening 32 we are going to draw an arc that will intersect with the line just drawn in a point we call 4. At this point we aim with the compass at 1 with opening 14 and draw the entire circumference that will circumscribe the decagon.
How do you divide a circumference into 10 parts?
- Fix points O, A and the segment OA (radius of the circumference);
- Plot the circumference with center in O and radius OA;
- Trace the line passing through the points O, A;
- Draw the line perpendicular to line 3. …
- Fix the intersection points of the straight line 4.
What is a 12-sided figure called?
dodecagon Convex polygon having 12 sides and 12 angles; in d. regular, with equal sides and angles, the latter have a width of 150 °.
How large is an outer corner of a polygon?
Theorem: the sum of the external angles of a convex polygon is equal to a round angle (360 °), whatever the number of its sides.
How do you calculate the external angle?
We therefore find a formula to calculate each external corner. This is “sum external angles = 360 / N”. In this case “N” means the number of sides of a polygon. For this, we also consider it as the number of corners.
How large is an external angle of an equilateral triangle?
Since we have carried out the proof without using any particular property, we can conclude that the sum of the external angles of any triangle is 360 °; whether it is scalene, isosceles, rectangle or equilateral does not matter.
How many vertices does a triangle have?
A triangle is a polygon with three sides and therefore three vertices and three internal angles.
How many vertices are there in a square?
mathematical quadrilateral In elementary geometry, the figure identified by 4 points (vertices) of a plane, considered in a given order, and by the 4 segments (sides) that join them in that order; the term is synonymous with quadrangle.
How many vertices does the Octagon have?
octagon In geometry, polygon (plane) having 8 vertices and therefore 8 sides. The. regular has 8 sides and 8 internal angles equal to each other; then each angle measures 135 ° (➔ polygon).
What is primary school apothem?
Apothem of a polygon is defined as the radius of the circumference inscribed in it. This radius assumes great importance especially in regular polygons, because it allows – regardless of the number of their sides – to easily calculate their perimeter and area.
How is the apothem of a right triangle calculated?
To calculate the apothem we want to use the inverse rule to obtain the area of a circumscribed polygon, just apply the formula: A = (P xa) / 2. From this we can obtain the inverse rule which will therefore be a = 2A / P.
How is the side calculated?
If the area of the square is known, to obtain the measurement of the side it is sufficient to extract the square root of the area. The area of a square is 225 square meters. Calculate the size of the side. To calculate the side of the square from the diagonal, divide the diagonal of the square by the root of 2.
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