What is the missing length l of the triangular prism of the surface area is 524 square centimeter 10cm, 10cm, 6cm, 8cm
A: 16 cm
B: 17 cm
C: 8 cm
D: 10 cm
17 cm
First, we need to calculate the lateral surface area of the triangular prism:
Lateral Surface Area = Perimeter of base * Height
Perimeter of base = 10 + 10 + 6 = 26 cm
Height = 8 cm
Lateral Surface Area = 26 * 8 = 208 cm^2
Now, we need to calculate the total surface area of the triangular prism:
Total Surface Area = Lateral Surface Area + 2(Base Area)
Base Area = (1/2) * Perimeter of base * Height
Base Area = (1/2) * 26 * 8
Base Area = 104 cm^2
Total Surface Area = 208 + 2(104)
Total Surface Area = 416 cm^2
Since the given total surface area is 524 cm^2, we need to find the missing length l:
Total Surface Area = 416 + 2(l * 10)
524 = 416 + 20l
108 = 20l
l = 5.4 cm
Therefore, the missing length l is not one of the given options.