Find the slant height of the square pyramid. Round to the nearest whole inch, if necessary.
a.17in
b.11in
c.8in
d.6in
To find the slant height of a square pyramid, we can use the Pythagorean theorem.
The slant height is the hypotenuse of a right triangle with one leg being the height of the pyramid and the other leg being half the length of one side of the base.
Since a square has all sides equal, half the length of one side of the base is equal to half the length of one side of the square.
Therefore, the slant height is given by:
hypotenuse = √(height^2 + (side length/2)^2)
Let's calculate the slant height for each option:
a) Slant height = √(17^2 + (17/2)^2) = √(289 + 144.5) = √(433.5) ≈ 20.81 in
b) Slant height = √(11^2 + (11/2)^2) = √(121 + 30.25) = √(151.25) ≈ 12.30 in
c) Slant height = √(8^2 + (8/2)^2) = √(64 + 16) = √(80) ≈ 8.94 in
d) Slant height = √(6^2 + (6/2)^2) = √(36 + 9) = √(45) ≈ 6.71 in
Rounding the slant heights to the nearest whole inch, we have:
a) 20 in
b) 12 in
c) 9 in
d) 7 in
Therefore, the correct answer is a) 17 in.