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What is the area of a regular hexagon with apothem 6?

Anonymous

∙ 15y ago

Updated: 4/28/2022

Draw incircle and circumcircle. radius of incircle = 6 radius of circumcircle = 6 × 2/√3 = 12/√3 (side opposite to 60° is √3/2 times hypotenuse. consider right angled triangle formed by these two radius and 1/2 side of hexagon. (1/2 side)² = (12/√3)² - 6² = 12 1/2 side = √12 full side of hexagon = 2√12, perimeter = 12√12 Area = 1/2 a × perimeter = 1/2 × 6 × 12√12 = 36√12 = 72√3 unit²

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∙ 15y ago

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Q: What is the area of a regular hexagon with apothem 6?

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What is the area of a regular hexagon with a side of 4 and an apothem of 3 46?

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.

Find the area of the regular hexagon described in the question above?

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.

What is the area of a regular hexagon if a side is 30?

The area is about 2338.27 square units, from the formulaA = 3/2 (sqrt 3) s2 or about 2.598 s2--Let's draw a segment from the center of the hexagon to the middle of a side. This segment is called the apothem. Then use the 30-60-90 triangle rule. If half of a side is 15, that means the apothem is 15√3.If we divide the hexagon into equilateral triangles, we get 6 equilateral triangles.So if we find the area for one of these triangles and multiply it by 6, we get the area of the hexagon. The area of a triangle is found by 1/2(b*h). The apothem is your height for the triangles. So plug the numbers in: 1/2(30*15√3). Solve: 1/2(779.4228) = 389.7114. This is the area of one triangle. Now we multiply by 6, and this becomes: 2338.2686

Area of a reagular hexagon if each side is 11m the apothem is 9 and radius 10?

We don't need the measure of the radius since we know the measure length of the side and of the apothem, which we use to find the area of one of the triangles that are formed by connecting the center with the vertices of the hexagon. So, A = 6[(1/2)(11 x 9)] = 297 m2

What is the perimeter of a hexagon with 27 cm sides?

If it's a regular hexagon then 6*27 = 162 cm

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Related Questions

What is the area of a regular hexagon with a side of 4 and an apothem of 3 46?

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.

What is the area of a regular hexagon with apothem length of 24 inches?

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

Find the area of the regular hexagon described in the question above?

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.

What is the area of a regular hexagon with a perimeter of 36 inches and an apothem of 5.2 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.]

What is the area of a regular hexagon with 19 inch apothem and 12 inch sides?

Hexagon is composed of 6 equilateral triangles of side 12in, or 12 right-angled triangles, in this case with sides 6, 12 and 19. Two of these make a rectangle 6 x 19 ie 114 sqin. there are 6 such rectangles so the total area is 684 sqin. The only problem is that no such hexagon is possible, as the side must be greater than the apothem to satisfy Pythagoras?

How do you calculate an area of a hexagon?

If it is a regular hexagon then make 6 triangles then find the area of one then multiply by 6.

What is the area of a regular hexagon if a side is 30?

The area is about 2338.27 square units, from the formulaA = 3/2 (sqrt 3) s2 or about 2.598 s2--Let's draw a segment from the center of the hexagon to the middle of a side. This segment is called the apothem. Then use the 30-60-90 triangle rule. If half of a side is 15, that means the apothem is 15√3.If we divide the hexagon into equilateral triangles, we get 6 equilateral triangles.So if we find the area for one of these triangles and multiply it by 6, we get the area of the hexagon. The area of a triangle is found by 1/2(b*h). The apothem is your height for the triangles. So plug the numbers in: 1/2(30*15√3). Solve: 1/2(779.4228) = 389.7114. This is the area of one triangle. Now we multiply by 6, and this becomes: 2338.2686

Find the area of a regular hexagon if its perimeter is 60 cm?

A hexagon has 6 sides. The area of a regular hexagon that has a perimeter of 60 cm is 259.81 cm squared.

What is the perimeter of a hexagon having 225 cm square area of a circle inscribed in it?

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

What is the apothem of a regular hexagon with sides of 16 inches?

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.

If a hexagon has an apothem of 1.7 inches and a perimeter of 12 inches about how many regular hexagons will it take to make a quilt that is 6 feet by 8 feet?

9762

What is the Relation between area of an equilateral triangle and area of a regular hexagon with same sides using activity method?

In our example, the area of the equilateral triangle is 1/6 of the area of the regular hexagon

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