Use the image to answer the question.
An illustration shows a triangular prism. The front triangular face is visible. The right rectangular face is visible. The sides and edges that are not visible are indicated by dashed lines. Parts are labeled with measurements. The left side of the triangle measures 10 centimeters. The right side of the triangle also measures 10 centimeters. The perpendicular height from the top vertex of the triangle to the base measures 6 centimeters. The base of the triangle measures 8 centimeters.
What is the missing length l
of the triangular prism if the surface area is 524 square centimeters
To find the missing length, we first need to calculate the surface area of the triangular prism.
The formula for the surface area of a triangular prism is:
Surface Area = 2*(area of triangle base) + (perimeter of base)*(height of prism)
First, calculate the area of the base triangle:
Area of base triangle = (1/2)*(base)*(height)
Area of base triangle = (1/2)*(8 cm)*(6 cm)
Area of base triangle = 24 square cm
Next, calculate the perimeter of the base triangle:
Perimeter of base = sum of all sides
Perimeter of base = 10 cm + 10 cm + 8 cm
Perimeter of base = 28 cm
Now, plug these values into the surface area formula:
Surface Area = 2*(24 square cm) + (28 cm)*(l)
Surface Area = 48 square cm + 28l square cm
Surface Area = 48 + 28l square cm
Given the total surface area is 524 square cm, we can now solve for l:
524 = 48 + 28l
476 = 28l
l = 17
Therefore, the missing length of the triangular prism is 17 cm.