10 cm
10 cm
6 cm
8 cm
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
The surface area of a triangular prism is given by the formula:
A = 2B + Ph
where A is the surface area, B is the area of one of the triangular bases, P is the perimeter of the base, and h is the height of the prism.
The base of the triangular prism is a triangle formed by sides of lengths 10 cm, 6 cm, and l. To find the area of this triangle, we can use Heron's formula:
A = sqrt(s*(s-10)*(s-6)*(s-l))
where s is the semi-perimeter of the triangle.
The area of one base will be half of the result from Heron's formula since the prism has two identical bases.
Let's use the given surface area A = 524 square centimeters and the known lengths of the sides to find the missing length l:
524 = 2*(1/2)*(10 cm)*(6 cm) + 10 cm + 6 cm + l
524 = 60 + 16 + l
524 = 76 + l
524 - 76 = l
448 = l
Therefore, the missing length l of the triangular prism is 448 cm.