SOLUTION: The base of right pyramid ABCDF is rhombus ABCD. Segment FK is the altitude of the pyramid. The angle between the lateral edge FB and FK is 36°. Find the area and the perimete

Algebra ->  Polygons -> SOLUTION: The base of right pyramid ABCDF is rhombus ABCD. Segment FK is the altitude of the pyramid. The angle between the lateral edge FB and FK is 36°. Find the area and the perimete      Log On


   

Question 1206859: The base of right pyramid ABCDF is
rhombus ABCD. Segment FK is the
altitude of the pyramid. The angle
between the lateral edge FB and FK is
36°. Find the area and the perimeter of
△BFD if the length of the smaller
diagonal BD is 10 cm. Round your
answer to the nearest cm .
Found 2 solutions by Edwin McCravy, mccravyedwin:
Answer by Edwin McCravy(20054) About Me  (Show Source):
Answer by mccravyedwin(406) About Me  (Show Source):
You can put this solution on YOUR website!



First find the area of triangle BFK, half of triangle BFD.

BD=10, so BK=5

BK%2F%28FK%29=tan%2836%5Eo%29

5%2F%28FK%29=tan%2836%5Eo%29

Fk%2Atan%2836%5Eo%29=5

FK=5%2Ftan%2836%5Eo%29

matrix%281%2C4%2CAREA%2COF%2CDELTA%2CBFK%29%22%22=%22%22expr%281%2F2%29BK%2AFK%22%22=%22%22expr%281%2F2%29%2A5%2A%285%2Ftan%2836%5Eo%29%29%22%22=%22%2225%2F%282tan%2836%5Eo%29%29

matrix%281%2C4%2CAREA%2COF%2CDELTA%2CBFD%29%22%22=%22%2225%2F%28tan%2836%5Eo%29%29%22%22=%22%22matrix%281%2C2%2C34.40954801%2Ccm%5E2%29

To find the perimeter, we need to find FB.

BD%2F%28FB%29=sin%2836%5Eo%29

5%2F%28FB%29=sin%2836%5Eo%29

FB%2Asin%2836%5Eo%29=5

FB=5%2Fsin%2836%5Eo%29=8.506508084=FD

matrix%281%2C4%2CAREA%2COF%2CDELTA%2CBFD%29%22%22=%22%2225%2F%28tan%2836%5Eo%29%29%22%22=%22%22matrix%281%2C2%2C34.40954801%2Ccm%5E2%29


matrix%281%2C2%2C34.40954801%2Ccm%5E2%29

matrix%281%2C4%2CPERIMETER%2COF%2CDELTA%2CBFD%29%22%22=%22%22FB%2BBD%2BFD%22%22=%22%228.506508084%2B10%2B8.506508084%22%22=%22%22matrix%281%2C2%2C27.01301617%2Ccm%29.

Rounding off to the nearest integer:

matrix%281%2C4%2CAREA%2COF%2CDELTA%2CBFD%29%22%22=%22%22matrix%281%2C2%2C34%2Ccm%5E2%29

matrix%281%2C4%2CPERIMETER%2COF%2CDELTA%2CBFD%29%22%22=%22%22matrix%281%2C2%2C27%2Ccm%29.

Edwin