Are you a genius then sove this....i can't

Look at triangle  ABE .  We know..

 

∠ABE  =  81°

AB  =  4 cm       and

BE  =  6 cm

 

So using the law of cosines...

 

AE²  =  6² + 4² - 2(6)(4) cos 81°

AE²  =  36 + 16 - 48 cos 81°

AE²  =  52 - 48 cos 81°          Take the positive square root of both sides.

AE  =  √[  52 - 48 cos 81°  ]    Plug this into a calculator to get...

AE  ≈   6.67

AE  ≈   6.7     cm

 

h, AE, and part of AC form a right triangle, and we know...

 

∠EAC  =  46°    and

AE  ≈  6.67       so...

 

sin 46°  =  h / AE

h   =   AE sin 46°

h   ≈   6.67sin 46°

h   ≈   4.8    cm

 

The base is a square with a side length of  4 cm  , so...

 

area of base =  (4 cm)²  =  16 cm²

height  =  h  ≈  4.8 cm

 

volume of pyramid  ≈  (1/3)(16 cm²)(4.8 cm)

volume of pyramid  ≈  25.6  cm³