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Nina [5.8K]
3 years ago
5

SURFACE AREAS – PYRAMIDS URGENT

Mathematics
1 answer:
soldier1979 [14.2K]3 years ago
3 0

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

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