In the rhombus ABCD AB = 10, the smaller diagonal AC is 12. Find the area of the rhombus.

A rhombus is a parallelogram in which all sides are equal and the angles are not right.

In order to find the area of ​​a rhombus, it is most convenient to use the formula for the area behind the diagonals:

S = 1/2 * d1 * d2, where:

S is the area of ​​the rhombus;

d1 is the length of the smaller AC diagonal;

d2 – the length of the larger diagonal BD.

To do this, you need to find the length of the larger diagonal BD.

The diagonals of the rhombus are perpendicular and the intersection point is halved:

AO = OC = AC / 2;

AO = OC = 12/2 = 6 cm;

BO = OD = BD / 2.

Consider the triangle ΔABO. This triangle is right-angled with a right angle ∠O.

We apply the Pythagorean theorem, according to which the square of the hypotenuse is equal to the sum of the squares of the legs:

AB ^ 2 = BO ^ 2 + AO ^ 2;

BO ^ 2 = AB ^ 2 – AO ^ 2;

BO ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64;

BO = √64 = 8 cm.

BD = BO ∙ 2;

ВD = 8 ∙ 2 = 16 cm.

S = 1/2 12 16 = 192/2 = 96 cm2.

Answer: the area of ​​the rhombus is 96 cm2.