2019 AMC 8 Problems/Problem 4
Revision as of 02:21, 20 November 2019 by Phoenixfire (talk | contribs) (Created page with "== Solution == <asy> draw((-13,0)--(0,5)); draw((0,5)--(13,0)); draw((13,0)--(0,-5)); draw((0,-5)--(-13,0)); draw((0,0)--(13,0)); draw((0,0)--(0,5)); draw((0,0)--(-13,0)); dra...")
Solution
Because it is a rhombus all sides are equal. Implies all sides are 13. In a rhombus diagonals are perpendicular and bisect each other.
Which means =
=
.
Consider one of the right triangles.
=
.
=
.
Which means
=
.
Thus the values of the two diagonals are =
and
=
.
Which means area =
=
=