14
297 M
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
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.
40K
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.
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.
To find the area of a regular hexagon, you can use the formula: Area = (Perimeter × Apothem) / 2. The perimeter of the hexagon is 6 times the side length, so for a side length of 2 cm, the perimeter is 12 cm. Substituting the values into the formula gives: Area = (12 cm × 1.7 cm) / 2 = 10.2 cm². Thus, the area of the hexagon is 10.2 cm².
the formula to find the area of any prism is to find the area of the base (a regular hexagon, meaning that all sides and angles are the same) and multiply by the height of the prism. To find the area of a hexagon you multiply the apothem by the perimeter of the hexagon, and then divide that by 2. the apothem is a line from the center point to the center of any side, forming a right angle with a side, it doesn't matter which one. Once you find the area of the hexagon, multiply it with the height.
Perimeter = 2*Area/Apothem.
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.
To find the area of the shaded region, we first need to calculate the area of the regular hexagon using the formula ( A_{hexagon} = \frac{3\sqrt{3}}{2} \times a^2 ), where ( a ) is the apothem. Given that the apothem is 15.59 units, the area of the hexagon is approximately ( A_{hexagon} = \frac{3\sqrt{3}}{2} \times (15.59)^2 \approx 610.23 ) square units. The area of the rectangle must be determined separately, and the area of the shaded region is found by subtracting the rectangle's area from the hexagon's area. Without the dimensions of the rectangle, the exact area of the shaded region cannot be calculated.
297 M
To find the area of the shaded region (the rectangle inside the hexagon), we first calculate the area of the hexagon using the formula ( \text{Area} = \frac{3\sqrt{3}}{2} \times a^2 ), where ( a ) is the apothem. Given that the apothem is 15.59 units, the area of the hexagon is approximately ( \frac{3\sqrt{3}}{2} \times (15.59^2) \approx 609.67 ) square units. Assuming the rectangle’s area is not specified, the shaded area would be the hexagon's area minus the rectangle's area. If the rectangle's area is provided, subtract it from the hexagon's area to find the shaded region's area.
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
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?
It is 679 square metres.
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.