Find the surface area of pyramid that has a regular hexagonal base od edge 6 cm and a height of 8 cm.
Thank you so much
To find the surface area of a pyramid, we need to add the areas of all the faces.
First, let's calculate the area of the base of the pyramid. Since the base is a regular hexagon, we can divide it into 6 congruent equilateral triangles.
To find the area of an equilateral triangle, we use the formula:
Area = (side length^2 * √3) / 4
In this case, the side length of the equilateral triangle is 6 cm.
So, the area of one equilateral triangle is:
Area_of_triangle = (6^2 * √3) / 4
Next, we find the area of the 6 triangles that make up the base:
Area_of_base = 6 * (6^2 * √3) / 4
Next, let's calculate the area of the lateral faces of the pyramid. These faces form the sides of the pyramid with the base. Each of these faces is a trapezoid.
To find the area of a trapezoid, we use the formula:
Area = [(base1 + base2) * height] / 2
In this case, the height of the trapezoid is 8 cm.
And the bases of the trapezoid are the side lengths of the hexagonal base, which is 6 cm.
So, the area of one trapezoid is:
Area_of_trapezoid = [(6 + 6) * 8] / 2
Next, we find the area of the 4 trapezoids that make up the lateral faces:
Area_of_lateral_faces = 4 * [(6 + 6) * 8] / 2
Finally, to find the total surface area of the pyramid, we add the area of the base and the area of the lateral faces:
Surface_area_of_pyramid = Area_of_base + Area_of_lateral_faces
Now, you can substitute the values into the formulas and calculate the surface area of the pyramid.