BCDE is a square with side lengths of 10cm , The other faces of the pyramids are equilateral triangles with side lengths of 10cm. a) calculate the volume of the pyramid? (3 s.f) (Apex= A , front triangles areB&C, back are E&D)

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Answer 1 · 2018-05-27T13:28:07

See Below.

MS Paint Artwork

First Join #BD#, and Draw a perpendicular #AF# on #BD#.

This is the height of the pyramid.

To find the height, we need to find other things first.

As #BCDE# is a square and #BD# is its diagonal,

#BD = sqrt(2) xx "Side Length" = 10sqrt(2)# cm.

Now, In #DeltaABD#,

#AB =AC= AD = 10 # cm [As Every triangle is equilateral].

So, #DeltaABD# is an isosceles triangle.

So, The Altitude = #AF = sqrt(10^2 - ((10sqrt(2))/2)^2)# cm #= sqrt(100 - (200/4))# cm #= sqrt(100 - 50)# cm = #sqrt(50)# cm = #5sqrt(2)# cm.

So, The Volume Of The Pyramid :-

#1/3 xx"Base" xx "Width"xx "Height" = (1/3 xx 10 xx 10 xx 5sqrt(2))# #cm^3# = #500/3sqrt(2)# #cm^3# = #235# #cm^3# (3 s.f.)

Hope this helps.