Find the area of an isosceles triangle with a side side of 17 m and a base of 16 m.

Given: isosceles triangle ABC; AB = 17 meters; AC = 16 meters.

Find: the area of ​​the triangle ABC.

Since ABC is an isosceles triangle, it means that AB = BC = 17 meters.

AC base = 16 meters – on condition.

The area of ​​a triangle is found by the formula:

S = 1/2 * a * h (where S is the area of ​​the triangle; h is the height; a is the side to which the height is drawn).

Let’s draw the height of the HV to the base of the speaker. Since triangle ABC is isosceles, BE is also the bisector and median.

Since BH is the median, it divides the base of the AC into two equal segments: AH = HC = 1/2 * 16 = 8 (meters).

By the Pythagorean theorem, we find the length of the height:

AB ^ 2 = BH ^ 2 + AH ^ 2;

16 ^ 2 = BH ^ 2 + 8 ^ 2;

BH ^ 2 = 256 + 64;

BH ^ 2 = 320;

BH = √320;

BH = 8√5.

S = 1/2 * a * h = 1/2 * 16 * 8√5 = 8 * 8√5 = 64√5 (meters ^ 2).

Answer: 64√5 meters ^ 2.