Given information:
- Height of the triangle: 31.4 mm
- Area of the triangle: 1256 mm²

Solution:

To find the value of the height of the triangle, we can use the formula for the area of a triangle:

Area = (base × height) / 2

In this case, the area is given as 1256 mm². Let's denote the base of the triangle as b. Therefore, the formula can be rewritten as:

1256 = (b × 31.4) / 2

Finding the base of the triangle:

To find the base of the triangle, we can rearrange the formula:

b = (2 * Area) / height

Substituting the given values into the formula, we get:

b = (2 * 1256) / 31.4
b = 80 mm

Calculating the value of the height:

Now that we have the base and the height of the triangle, we can find the value of the height. Using the formula for the area of a triangle, we have:

Area = (base × height) / 2

Substituting the known values, we get:

1256 = (80 × height) / 2

Simplifying the equation:

1256 = 40 × height

Dividing both sides by 40:

31.4 = height

Therefore, the value of the height of the triangle is 31.4 mm.

Summary:

- The base of the triangle is found to be 80 mm.
- The height of the triangle is calculated to be 31.4 mm.
- The area of the triangle is given as 1256 mm².
- The calculations are based on the formula for the area of a triangle: Area = (base × height) / 2.