Answer:
The surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.
Explanation:
formulas:
Surface Area = 2B + Ph
Volume = Bh
where B is the area of the triangular base, P is the perimeter of the base, h is the height of the prism, and B and h are both in the same units (inches, feet, etc.).
Given:
Height of the triangular prism = 1 foot
Base of the triangular prism = 6 inches
Height of the triangular base = 4 inches
Length of the other two sides of the triangular base = 5 inches
First, we need to find the area of the triangular base (B):
B = (1/2) x base x height
B = (1/2) x 6 inches x 4 inches
B = 12 square inches
Next, we need to find the perimeter of the triangular base (P):
P = sum of all three sides
P = 6 inches + 5 inches + 5 inches
P = 16 inches
Now, we can use the formulas to find the surface area and volume:
Surface Area = 2B + Ph
Surface Area = 2(12 square inches) + (16 inches)(1 foot)
Surface Area = 24 square inches + 16 square feet
Surface Area = 16.222 square feet (rounded to three decimal places)
Volume = Bh
Volume = 12 square inches x 1 foot
Volume = 12 cubic feet
Therefore, the surface area of the triangular prism is approximately 16.222 square feet, and the volume of the triangular prism is 12 cubic feet.