The perimeter of a triangle is 70 and the radius of the inscribed circle is 4. Find the area of this triangle.

Let’s use the formula for the area of ​​a triangle in terms of the radius of a circle inscribed in this triangle:

S = p * r,

where S is the area of ​​the triangle, p is the half-perimeter of the triangle, equal to the half-sum of all sides of this triangle, and r is the radius of the circle inscribed in this triangle.

According to the condition of the problem, the perimeter of this triangle is 70, and the radius of the circle inscribed in this triangle is 4.

Therefore, the half-perimeter of this triangle is 70/2 = 35, and the area S of this triangle is:

S = 35 * 4 = 140.

Answer: the area of ​​this triangle is 140.