# 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 a rhombus. if the side of the rhombus is 6cm. The answer should be 18√3cm²**

Given:

rhombus ABCE,

AO – the height drawn to the side of the aircraft,

ВO = OС,

AB = 6 centimeters.

Find the area of the rhombus ABCE, that is, S ABCE -?

Solution:

1. Consider a right-angled triangle AOB.

Then, by the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

AO ^ 2 + BO ^ 2 = AB ^ 2:

AO ^ 2 + 3 ^ 2 = 6 ^ 2;

AO ^ 2 + 9 = 36;

AO ^ 2 = 36 – 9;

AO ^ 2 = 27;

AO = 3 √3 centimeters.

2. The area of a rhombus is equal to the product of the height by the side to which it is drawn, that is

S ABCE = AO * BC;

S ABCE = 3 √3 * 6;

S ABCE = 18 √3 cm ^ 2.

Answer: 18 √3 cm ^ 2.