1. Find the surface area for the given prism.
Length: 14 in.
Width: 10 in.
Height: 8 in.
A. 564 in^2
B. 664 in^2
C. 1,120 in^2
D. 1,080 in^2
SA = 2ab + 2bc + 2ac - (a is 14, b is 10, and c is 8.)
= (2*14*10) + (2*10*8) + (2*14*8)
= 280 + 160 + 224
= 664
Yes
To find the surface area of a prism, we need to find the area of each individual face and then sum them up.
The given prism has a length of 14 in, a width of 10 in, and a height of 8 in.
1. To find the area of the rectangular base, multiply the length by the width:
Area of base = length * width = 14 in * 10 in = 140 in^2
2. The prism has two identical rectangular faces on the top and bottom, so the combined area of the two is twice the area of the base:
Area of top and bottom faces = 2 * Area of base = 2 * 140 in^2 = 280 in^2
3. The prism also has four identical rectangular faces on the sides, so the combined area of the four sides is four times the area of the base:
Area of side faces = 4 * Area of base = 4 * 140 in^2 = 560 in^2
4. To find the total surface area, add the areas of the top, bottom, and side faces:
Total surface area = Area of top and bottom faces + Area of side faces
Total surface area = 280 in^2 + 560 in^2 = 840 in^2.
Therefore, the correct surface area for the given prism is 840 in^2.
None of the provided options match the correct surface area, so none of them are the correct answer.
To find the surface area of a prism, we need to calculate the sum of the areas of all its faces.
For this rectangular prism, we have six faces: two rectangular faces on the top and bottom, and four rectangular faces on the sides.
1. To find the area of the top and bottom faces, we multiply the length by the width:
Area of top face = Length * Width = 14 in * 10 in = 140 in^2
Area of bottom face = Length * Width = 14 in * 10 in = 140 in^2
2. To find the area of the four side faces, we need to calculate the perimeter of the rectangular base and multiply it by the height. The perimeter of a rectangle can be found by adding the lengths of all four sides:
Perimeter of the base = 2 * (Length + Width) = 2 * (14 in + 10 in) = 2 * 24 in = 48 in
Area of one side face = Perimeter of base * Height = 48 in * 8 in = 384 in^2
3. Finally, we add up all the areas to find the total surface area:
Total surface area = 2 * (Area of top face + Area of bottom face) + Area of four side faces
= 2 * (140 in^2 + 140 in^2) + 384 in^2
= 2 * 280 in^2 + 384 in^2
= 560 in^2 + 384 in^2
= 944 in^2
Therefore, the correct answer is not among the options provided. The surface area of the given prism is 944 in^2.