Question

Plz help ill give u brainlist

Answer 1

The surface area of a shape is the sum of the areas of the surfaces of a shape. 

If you break the surface are of your regular hexagonal pyramid down, you'll find that it's created from the sum of (see picture):
1) The area of one regular hexagon (the base), which is made up of 6 equilateral triangles, plus
2) The area of six triangles (the sides of the pyramid)

To find the total surface area, just find the area of the hexagonal base and add the area of the six triangular sides!
1) Area of the hexagonal base:
There are six equilateral triangles making up this hexagon. The equation for the area of each triangle is $A = \frac{1}{2} bh$, and you're already given the base, b=9cm, and height, h=7.8cm. Plug these values in and solve for the area of one equilateral triangle:
$A = \frac{1}{2} bh\\ A = \frac{1}{2} (9\:cm)(7.8\:cm)\\ A = 35.1 \: cm^{2}$

Now multiply $35.1 \: cm^{2}$ by 6, since there are six triangles of the same size, to get the area of the hexagonal base:
$35.1 \: cm^{2} \times 6 = 210.6 \: cm^{2}$

2) Total area of the triangular sides
Use the equation for the area of a triangle again, $A = \frac{1}{2} bh$. You are told that the base of each triangle, b=9cm, and the height, h=10cm. Plug that into the equation and solve for the area of one of the triangular sides:
$A = \frac{1}{2} bh\\ A = \frac{1}{2} (9\:cm)(10\:cm)\\ A = 45 \: cm^{2}$

Now multiply $45 \: cm^{2}$ by 6 because there are six triangular sides:
$45 \: cm^{2} \times 6 = 270\: cm^{2}$

3) Add the area of the hexagonal base and area of the six triangular sides to find the total surface area of the hexagonal pyramid:
$210.6 \: cm^{2} + 270\: cm^{2} = 480.6 \: cm^{2}$

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Answer: 480.6 $cm^{2}$