Answer:
the total surface area of the prism is 374.8 cm^2.
Explanation:
Since the cross-section is an equilateral triangle of side 6 cm, the area of the triangle is:
A = 1/2 * base * height = 1/2 * 6 cm * 5.2 cm = 15.6 cm^2
where 5.2 cm is the height of the equilateral triangle.
The total surface area of the prism consists of the area of the two equilateral triangles and the area of the three rectangular faces. The area of each rectangular face is the product of its length and width.
The length of the prism is 20 cm and the width of each rectangular face is 6 cm, so the area of each rectangular face is:
A_rect = length * width = 20 cm * 6 cm = 120 cm^2
Therefore, the total surface area of the prism is:
A_total = 2 * A_tri + 3 * A_rect
= 2 * 15.6 cm^2 + 3 * 120 cm^2
= 374.8 cm^2
Hence, the total surface area of the prism is 374.8 cm^2.