The height lowered from the top of the obtuse angle of the rhombus divides the side to which it is lowered

The height lowered from the top of the obtuse angle of the rhombus divides the side to which it is lowered into two equal parts. Find the area of the rhombus if the side of the rhombus is 6cm

Given:
rhombus ABCE,
АН – height,
BH = HC,
AB = 6 centimeters,
Find the area of a rhombus S ABCE -?
Decision:
1) Consider a right-angled triangle ABN. Side BН = HC = 1/2 * 6 = 6/2 = 3 (centimeters). By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):
AH ^ 2 + BH ^ 2 = AB ^ 2 (we express the legs AH ^ 2 from this equality);
AH ^ 2 = AB ^ 2 – BH ^ 2;
AH ^ 2 = 6 ^ 2 – 3 ^ 2;
AH ^ 2 = 36 – 9;
AH ^ 2 = 27;
AH = √27;
AH = 3√3;
2) Consider a rhombus ABCE.
S ABCE = AН * BC;
S ABCE = 3√3 * 6;
S ABCE = 18√3 square centimeters.
Answer: 18√3 square centimeters.