Find the surface area of the prism. Round to the nearest tenth if necessary. The three sides are all 8.1 inches, the area of the base is 28.4 inches^2, and 12 inches is the length. It's a,b,c, or d. A. 348.4 in^2 B. 320 in^2 C. 291.6 in^2 D. 251.2 in^2
find the surface area of each rectangular prism. round to nearest tenth if necessary. The top is 12ft the height is 1.7ft and the bottom is 6.4ft
To find the surface area of the prism, we need to calculate the area of the three rectangular faces and the area of the two triangular faces.
The area of a rectangular face is given by the formula: length x width.
Since all three sides of the rectangular face are 8.1 inches, the area of one rectangular face is 8.1 x 8.1 = 65.61 square inches.
Since the prism has three rectangular faces, the total area of the rectangular faces is 3 x 65.61 = 196.83 square inches.
The area of a triangular face can be found using the formula: (base x height) / 2.
For the triangular face, the base is 8.1 inches (same as the side length) and the height can be found using the Pythagorean theorem:
height = √(side ^ 2 - (base / 2) ^ 2) = √(8.1 ^ 2 - (8.1 / 2) ^ 2) = √(65.61 - 16.4025) = √49.2075 = 7 inches (rounded to the nearest whole number).
So, the area of one triangular face is (8.1 x 7) / 2 = 56.7 / 2 = 28.35 square inches.
Since the prism has two triangular faces, the total area of the triangular faces is 2 x 28.35 = 56.7 square inches.
Finally, we can find the surface area of the prism by adding the area of the rectangular faces and the area of the triangular faces:
Surface area = area of rectangular faces + area of triangular faces
Surface area = 196.83 + 56.7 = 253.53 square inches.
Rounded to the nearest tenth, the surface area of the prism is approximately 253.5 square inches.
Therefore, the correct option is D. 251.2 in^2
To find the surface area of a prism, you need to calculate the area of all its faces and then sum them up. In this case, the prism has three rectangular sides and two identical bases.
To calculate the area of each rectangular side, you need to multiply the length of the side by the height of the prism. The height is given as 12 inches, so the area of each rectangular side is 8.1 inches (the side length) multiplied by 12 inches (the height), which equals 97.2 square inches.
Next, you calculate the area of one base. It is given as 28.4 square inches.
Since the prism has two identical bases, the total area of the bases is 2 times 28.4 square inches, which equals 56.8 square inches.
Lastly, you add up the area of all the faces to find the total surface area. In this case, it is the sum of the areas of the three rectangular sides and the two bases.
Total surface area = (area of rectangular sides) + (area of bases)
= (3 * 97.2 square inches) + (56.8 square inches)
= 291.6 square inches.
Therefore, the surface area of the prism is 291.6 square inches.
Hence, the correct answer is C. 291.6 in^2.
the three long faces are 8.1x12 rectangles, so the total area is 3 faces + 2 bases:
3*8.1*12 + 2*28.4 = 291.6
Looks like C to me.