The surface area of a triangular prism can be calculated using the formula:
Surface Area = 2(Area of Base) + (Perimeter of Base) x (Height of Prism)
where the base of the triangular prism is a triangle and its height is the distance between the two parallel bases.
Given the measurements of the triangular prism as 10 cm, 6 cm, 8 cm, and 14 cm, we can find the surface area as follows:
- The base of the triangular prism is a triangle, so we need to find its area. Using the formula for the area of a triangle, we get:
Area of Base = (1/2) x Base x Height
where Base = 10 cm and Height = 6 cm (since the height of the triangle is perpendicular to the base). Plugging in these values, we get:
Area of Base = (1/2) x 10 cm x 6 cm = 30 cm^2
- The perimeter of the base can be found by adding up the lengths of the three sides of the triangle. Using the given measurements, we get:
Perimeter of Base = 10 cm + 6 cm + 8 cm = 24 cm
- The height of the prism is given as 14 cm.
Now we can plug in the values we found into the formula for surface area and get:
Surface Area = 2(Area of Base) + (Perimeter of Base) x (Height of Prism)
Surface Area = 2(30 cm^2) + (24 cm) x (14 cm)
Surface Area = 60 cm^2 + 336 cm^2
Surface Area = 396 cm^2
Therefore, the surface area of the triangular prism is 396 cm^2.