Find the length of d in the figure below if a = 8 in., b = 3 in., and c = 4 in. Round your answer to the nearest tenth. Pls help :(

Length of side 'd' = 9.4 in.

Step-by-step explanation:

From the picture attached,

Length of the sides of the given prism,

a = 8 in.

b = 3 in.

c = 4 in.

We have to find the measure of side 'd'.

By applying Pythagoras theorem in right triangle ABC,

AC² = AB² + BC²

AC =

     =

     =

     =

Now we apply Pythagoras theorem in right triagle ΔACE,

AE² = AC² + EC²

d² = + c²

d² = 73 + (4)²

d² = 89

d = √89

  = 9.43

  ≈ 9.4 in.

Therefore, length of side 'd' is 9.4 in.

256π units²   (answer b)

step-by-step explanation:

the formula for the surface area of a sphere of radius r

is             a = 4πr²

and so, if r = 8 units, then the surface area is:

a = 4π(8 units)² = 256π units²   (answer b)