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.