3.5 cm
3.9 cm
4.5 cm
Find the surface area of the solid figure with an equilateral triangle base.
(1 point)
First, we need to calculate the area of the equilateral triangle base. Since all sides of an equilateral triangle are equal, we can use the formula for the area of an equilateral triangle, which is A = (s^2 * √3) / 4, where s is the length of one side.
Given that the side length of the equilateral triangle base is 3.5 cm, we can plug in this value into the formula:
A = (3.5^2 * √3) / 4
A = (12.25 * √3) / 4
A = 3.0625√3 cm^2
Next, we need to calculate the lateral surface area of the solid figure. Since the solid figure has a triangular base and the height is 4.5 cm, the lateral surface area can be calculated using the formula of lateral surface area of a triangular prism, which is LSA = base perimeter * height.
Since the base is an equilateral triangle, the perimeter is simply 3 times the side length: 3 * 3.5 cm = 10.5 cm.
Now, we can calculate the lateral surface area:
LSA = 10.5 cm * 4.5 cm
LSA = 47.25 cm^2
Therefore, the surface area of the solid figure with an equilateral triangle base is the sum of the area of the base and the lateral surface area:
Surface Area = A + LSA
Surface Area = 3.0625√3 cm^2 + 47.25 cm^2
Surface Area ≈ 60.79 cm^2
So, the surface area of the solid figure with an equilateral triangle base is approximately 60.79 cm^2.