What is the missing length l of the triangular prism if the surface area is 524 square centimeters?10cm 10cm 6cm 8cm (1 point)Responses8 cm8 cm10 cm10 cm17 cm17 cm16 cm
To find the missing length of the triangular prism, we first need to calculate the surface area of each individual face, and then find the total surface area.
The formula to calculate the surface area of a triangular prism is:
Surface Area = 2(base area) + (perimeter of the base) * height
Given the dimensions of the triangular prism:
base triangle: base = 10 cm, height = 8 cm
rectangle: length = 10 cm, width = 6 cm
total height of the prism = l cm
Surface Area of the triangular base = (1/2) * base * height = (1/2) * 10 * 8 = 40 cm^2
Surface Area of the rectangle = length * width = 10 * 6 = 60 cm^2
Perimeter of the base triangle = sum of all sides = 10 + 10 + 6 = 26 cm
Given total surface area = 524 cm^2
524 = 2(40) + 26 * l
524 = 80 + 26l
26l = 524 - 80
26l = 444
l = 444 / 26
l = 17.08 cm
Therefore, the missing length of the triangular prism is approximately 17 cm.