The side of an isosceles triangle is 10 and the base is 12. Find the area of this triangle.

Given:

isosceles triangle ABC,

AB and BC – lateral sides,

AB = 10,

АС – base,

AC = 12.

Find the area of an isosceles triangle ABC -?

Decision:

Consider an isosceles triangle ABC. Let’s draw the height of the AO. She is the median. Therefore AO = OS = 12: 2 = 6.

Consider a right-angled triangle ABO. By the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):

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

BO ^ 2 = AB ^ 2 – AO ^ 2;

VO ^ 2 = 100 – 36;

BO ^ 2 = 64;

VO = 8.

S ABC = 1/2 * BO * AC;

S ABC = 1/2 * 8 * 12;

S ABC = 4 * 12;

S ABC = 48.

Answer: 48.