10 cm
10 cm
6 cm
COURSE TOOLS
8 cm
8:00
LESSON FEEDBACK
What is the missing length l of the triangular prism if the surface area is 524 square centimeters?
(1 point)
• 17 cm
• 10 cm
• 8 cm
• 16 cm
To find the missing length l of the triangular prism, we first need to calculate the surface area of the prism using the formula:
Surface Area = 2(lw + lh + wh)
Given that the surface area is 524 square centimeters, and that the lengths of the prism are 10 cm, 10 cm, and 6 cm, we can substitute these values into the formula:
524 = 2(10w + 10h + 6w)
262 = 10w + 10h + 6w
262 = 16w + 10h
We know that w = 10 and h = 6, so we can substitute those values into the equation:
262 = 16(10) + 10(6)
262 = 160 + 60
262 = 220
Now we can solve for the missing length l:
262 = 16w + 10(6)
262 = 16w + 60
202 = 16w
w = 202 / 16
w = 12.625
Therefore, the missing length l of the triangular prism is approximately 12.625 cm.
None of the given answer choices matches this result. So, none of the provided answer choices (17 cm, 10 cm, 8 cm, 16 cm) is correct.