Question

SURFACE AREAS – PYRAMIDS URGENT

Answer 1

In this question , to find the total surface area , we have to find the area of all faces and add them .

And here the base is a hexagon. THe formula of area of hexagon is

`(3 \sqrt 3)/(2) a^2`

And in the given diagram, side length , a=4cm , so area is

`(3 \sqrt 3)/(2) (4)^2 = 24 \sqrt 3`

Now we need to find the area of triangle.

We have 6 triangular faces. And for area of triangle, we need the slant edge, and for that we use pythagorean formula

`image`

Now we use the formula of area of triangle which is half times the product of base times height. And since there are 6 triangles, so we have to multiply by 6 too.

`=6*(1/2)*4*2 √(19) = 104.61`

So total surface area is

`24 \sqrt 3 + 104.61 =146.2 cm^2`