what is the area of the solid figure with an equilateral triangle base the numbers are 3.5 and 3.9 and 4.5
To find the area of the solid figure with an equilateral triangle base, we first need to calculate the area of the equilateral triangle base.
Since the three sides of the equilateral triangle are 3.5, 3.9, and 4.5, we know that all three sides are equal. Let's call each side length "s".
To find the height of the equilateral triangle, we can use the formula:
height = s * sqrt(3) / 2
In this case, the height of the equilateral triangle can be calculated by using any of the sides as they are all equal. Let's use 3.5:
height = 3.5 * sqrt(3) / 2 ≈ 3.03
Now, we can calculate the area of the equilateral triangle base using the formula:
Area = (base * height) / 2
Area = (3.5 * 3.03) / 2 ≈ 5.31
Now, the total area of the solid figure can be calculated by adding the area of the equilateral triangle base to the area of the three lateral faces. Since the lateral faces are all triangles with the same height as the base, we can calculate their combined area as:
Area_lateral = 3 * (3.03 * 3.9) / 2 ≈ 14.08
Therefore, the total area of the solid figure is:
5.31 (base area) + 14.08 (lateral faces area) ≈ 19.39
So, the area of the solid figure is approximately 19.39 square units.