SOLUTION: in rhombus ABCD, AB=14 and AC=20. Find the area of the rhombus to the nearest tenth

Algebra ->  Surface-area -> SOLUTION: in rhombus ABCD, AB=14 and AC=20. Find the area of the rhombus to the nearest tenth      Log On


   

Question 382856: in rhombus ABCD, AB=14 and AC=20. Find the area of the rhombus to the nearest tenth
Answer by richard1234(7193) About Me  (Show Source):
You can put this solution on YOUR website!
Since AB = 14, then BC and all other side lengths are 14. The diagonal AC is 20, so I'll find the area of ABC using Heron's formula:
A(ABC) = sqrt%28%2824%29%284%29%2810%29%2810%29%29+=+10+sqrt%2896%29+=+40+sqrt%286%29
However, ABC is only half the area of the rhombus, so the area of the rhombus is 80+sqrt%286%29 = 196.0 (to nearest tenth)