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.
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 -?
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.
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