A right rectangular pyramid is shown. The height of the pyramid is 12 units. The length and width of the base are 6 units and 8 units, as shown. Point F is the midpoint of line segment AB. Point E is directly above the center of rectangle ABCD.
Round all answers to the nearest hundredth place, if necessary.
The length of segment DB is ___ units.
The length of segment EB is ___ units.
The length of segment EF is about ___ units.
To find the length of segment DB, we can use the Pythagorean theorem on the right triangle DBC.
DB^2 = DC^2 + BC^2
DB^2 = 6^2 + 8^2
DB^2 = 36 + 64
DB^2 = 100
DB = 10 units
So, the length of segment DB is 10 units.
Next, to find the length of segment EB, we can use the height of the pyramid (12 units) as the other leg of a right triangle with segment EB as the hypotenuse.
EB^2 = EF^2 + FB^2
EB^2 = 12^2 + 3^2
EB^2 = 144 + 9
EB^2 = 153
EB ≈ 12.37 units
So, the length of segment EB is approximately 12.37 units.
Finally, to find the length of segment EF, we can use the Pythagorean theorem on the right triangle EFB.
EF^2 = EB^2 + BF^2
EF^2 = 12^2 + 3^2
EF^2 = 144 + 9
EF^2 = 153
EF ≈ 12.37 units
So, the length of segment EF is about 12.37 units.