A frustum of a square pyramid has an upper base edge of 6 cm and a lower base edge of 4 cm if the distance between these 2 bases is 10 cm. Find the total surface area of the frustum.
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Expert's answer
2021-08-19T08:00:51-0400
let small height, h = xcm
let big height, H=(10+x)
x10+x=46
40+4x=6x
2x=40
x=h=20
H=10+20=30cm
for the small pyramid, height of one face =202+22=20.1cm
=202+22=20.1cm
areaofface=1/2×4×20.1=40.2cm2
area of the four faces =40.2×4=160.8cm2
for the big pyramid, height of one face=302+32=30.15cm
302+32=30.15cm
area of the face =1/2×6×30.15=90.45cm2
area of four faces=90.45×4=361.8cm2
area of sides of frustum=361.8-160.8=201
assuming the frustum is closed both sides area of upper base =6×6=36cm2
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