Rhombus ABCD has perimeter 148, and one of its diagonals has length 28. what is the area of ABCD?
+1633 Because ABCD is a rhombus, then AB = BC = CD = AD.
AB = BC = CD = AD = 37 units.
One of rhombus ABCD's diagonals has length 28. We can divide 28 by 2 to get 14, which is the leg of a right triangle when rhombus ABCD is split into 4 congruent triangles.
The hypotenuse is 37, and the leg is 14, so that means the other leg is:√372−142 = √1173. Ew that looks ugly, but it is correct. That means the other diagonal has length 2√1173.
Since the area of a rhombus is one diagonal length times the other diagonal length over 2, then the area of this rhombus would be 28√1173 units squared.
