To find the area of the isosceles triangle, we can use the formula:
Area = (1/2) * base * height
Given that the base is 16 meters and the equal sides are each 17 meters, we can divide the triangle into two right triangles by drawing an altitude from the vertex opposite the base to the midpoint of the base.
Since the altitude bisects the base, each half of the base is 8 meters.
Now, we can use the Pythagorean theorem to find the height of each right triangle:
h^2 + 8^2 = 17^2
h^2 + 64 = 289
h^2 = 289 - 64
h^2 = 225
h = √225
h = 15
Now that we have the height, we can calculate the area of one half of the triangle:
Area = (1/2) * 8 * 15
Area = 60
Since the triangle consists of two congruent halves, the total area of the isosceles triangle is:
Total Area = 2 * 60
Total Area = 120
So, the area of the isosceles triangle is 120 square meters.
