The question cannot be answered.
A regular hexagon with sides of 10 inches would have apothems of 10/sqrt(2) = 7.071 inches. Therefore the hexagon cannot be regular.
And, since the hexagon is irregular, there is not enough information to answer the question.
For a regular hexagon, half the side length can be calculated from the apothem via trigonometry: half_side_length = apothem x tan 30° Then: area = apothem x 1/2 x perimeter = apothem x 1/2 x side_length x 6 = apothem x half_side_length x 6 = 24 in x (24 in x tan 30°) x 6 ≈ 1995 sq in
If the hexagon has side length s, then the apothem is sqrt(3) * s / 2.
Such a hexagon is impossible. A regular hexagon with sides of 2 cm can have an apothem of sqrt(3) cm = approx 1.73.It seems you got your question garbled. A regular hexagon, with sides of 2 cm, has an area of 10.4 sq cm. If you used your measurement units properly, you would have noticed that the 10.4 was associated with square units and it had to refer to an area, not a length.
The area of a given hexagon is equal to the area of an equilateral triangle whose perimeter is 36 inches. Find the length of a side of the regular hexagon.Click once to select an item at the bottom of the problem.
386.5
It is 665.1 sq inches.
Given the perimeter of a regular hexagon, it is better to use the side length: 6 inches, rather than the apothem of 5.2 inches because the latter is he rounded value of 3*sqrt(3) which is 5.196152... rather than 5.2. Based on the length of the sides, the area is approx 93.53 sq inches. [The apothem would have given 93.67 sq inches.]
665.1 square units.
By joining all the vertices to the centre of the octagon, the apothem forms the height of the triangles with the side of the regular octagon as the base. This the area is 8 × area_triangles = 8 × ½ × side × apothem = 4 × side × apothem: Area_regular_octagon = 4 × side_length × apothem ≈ 4 × 4 in × 4.8 in = 76.8 in²
For a regular hexagon, half the side length can be calculated from the apothem via trigonometry: half_side_length = apothem x tan 30° Then: area = apothem x 1/2 x perimeter = apothem x 1/2 x side_length x 6 = apothem x half_side_length x 6 = 24 in x (24 in x tan 30°) x 6 ≈ 1995 sq in
If the hexagon has side length s, then the apothem is sqrt(3) * s / 2.
12 x 5 x 20 ie 1200squnits. I'm not convinced you can have such a hexagon, if the side is 10 then shouldn't the apothem have to be 5 root 3?
Let s be the length of a side of the hexagon and let h be the the apothem 6(1/2sh) it the area of 3sh.
5.7735026918962... The formula for the area of a hexagon is A=.5ap, or A=(1/2)ap, where A=area, a=apothem, and p=perimeter. This means that, because the area is 100, 100=.5ap, so 200=ap. Because in a regular hexagon the apothem is equal to the side length, what we are really saying here is that 200=6a2. Therefore, 33.333=a2, or a= about 5.77. This is the side length.
Area of circle = 225 cm2 implies radius = 8.46 cm (approx) Therefore, apothem of hexagon = 8.46 cm then side of hexagon = apothem*2/sqrt(3) = 9.77 cm (approx) and so perimeter = 6*side = 58.63 cm
Easy. Since the side is the base and the apothem is the height of the triangle, multiply them and divide by two to get the area of the triangle. 3 * 3.46 = 10.38 /2 = 5.19. Then multiply by 6 to get the area of the hexagon. 5.19 * 6 = 31.14. You multiply by 6 because you can fit 6 regular triangles in a regular hexagon. We've already found the area of one regular triangle in the hexagon.
We know that the height of an equilateral triangle equals the product of one half of the side length measure with square root of 3.Since in our regular hexagon we form 6 equilateral triangles with sides length of 16 inches, the apothem length equals to 8√3 inches.