Use the image to answer the question. What is the missing length%C2%A0 l %C2%A0of the triangular prism if the surface area is%C2%A0524 square centimeters? (1 point) Responses 10 cm 10 cm 17 cm 17 cm 16 cm 16 cm 8 cm 8 cm Skip to navigation
To find the missing length l of the triangular prism, we first need to find the surface area of the prism.
The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2*(base area of the prism) + (perimeter of the base)*(height of the prism)
The base of the prism is a triangle with base 8 cm and height 6 cm, so the base area of the triangle is:
Base Area = 1/2 * base * height = 1/2 * 8 cm * 6 cm = 24 cm^2
The perimeter of the base is the sum of the three sides of the triangle:
Perimeter = 8 cm + 8 cm + 10 cm = 26 cm
Given that the surface area of the prism is 524 square centimeters, we can set up the equation:
524 = 2*24 + 26*l
524 = 48 + 26*l
476 = 26*l
l = 476 / 26
l = 18.31
Therefore, the missing length l of the triangular prism is approximately 18 cm.
not an option
I apologize for the error in my previous calculation. Let's recalculate:
Given:
Surface Area = 524 square centimeters
The triangular base of the prism has dimensions 8 cm by 10 cm with a height of 6 cm.
Base Area = 1/2 * base * height = 1/2 * 8 cm * 6 cm = 24 cm^2
The perimeter of the base is the sum of the three sides of the triangle:
Perimeter = 8 cm + 8 cm + 10 cm = 26 cm
Since the prism has two identical triangular faces, the total surface area of the prism is:
2 * (Base Area) + Perimeter * Height = 2 * 24 cm^2 + 26 cm * 6 cm = 48 cm^2 + 156 cm = 204 cm^2
But the total surface area of the prism is given as 524 square centimeters:
524 cm^2 = 2 * 24 cm^2 + 26 cm * l
524 cm^2 = 48 cm^2 + 26 cm * l
476 cm^2 = 26 cm * l
l = 476 cm^2 / 26 cm
l ≈ 18.31 cm
Therefore, the correct missing length l of the triangular prism is approximately 18.31 cm, which is not an exact option listed.