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

$\frac{3 \sqrt 3}{2} a^2$

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

$\frac{3 \sqrt 3}{2} (4)^2 = 24 \sqrt 3$

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

$8^2+(2 \sqrt 3)^2=h^2 \\ h^2 =76 \\ h = 2 \sqrt{19}$

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.

$=6*(1/2)*4*2 \sqrt{19} = 104.61$

So total surface area is

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