1. Find the surface area for the given prism. (1 point)
14 in.
8 in.
10 in.
O 564 in²
O 664 in²
O 1,120 in²
O 1,080 in²
AAAaannndd the bot gets it wrong yet again!
14*8*10 = 1120
To find the surface area of a prism, we need to calculate the sum of the areas of all its faces.
Given the dimensions of the prism:
Length = 14 in
Width = 8 in
Height = 10 in
First, let's calculate the area of the two bases (the top and bottom faces of the prism). The base is a rectangle, so the area can be calculated as length times width:
Area of base = Length x Width
Area of base = 14 in x 8 in
Area of base = 112 in²
Next, let's calculate the area of the four lateral faces (the sides of the prism). The lateral faces are also rectangles, so the area can be calculated as the perimeter of the base times the height:
Perimeter of base = 2 x (Length + Width)
Perimeter of base = 2 x (14 in + 8 in)
Perimeter of base = 2 x (22 in)
Perimeter of base = 44 in
Area of lateral face = Perimeter of base x Height
Area of lateral face = 44 in x 10 in
Area of lateral face = 440 in²
Finally, let's find the total surface area by adding the area of the two bases and the area of the four lateral faces:
Total Surface Area = 2(Area of base) + 4(Area of lateral face)
Total Surface Area = 2(112 in²) + 4(440 in²)
Total Surface Area = 224 in² + 1760 in²
Total Surface Area = 1984 in²
Therefore, the surface area of the given prism is 1984 in².
To find the surface area of a prism, first, we need to understand the formula for calculating the surface of a prism.
The surface area of a prism is given by the formula:
Surface Area = 2(Abase) + (Ph), where Abase is the area of the base of the prism, and Ph is the product of the perimeter of the base (P) and the height (h) of the prism.
In the given information, we have the dimensions of the prism:
Length (L) = 14 inches
Width (W) = 8 inches
Height (H) = 10 inches
1. Calculating the area of the base:
The base of the prism is a rectangle with dimensions Length (L) and Width (W).
Area of the base (Abase) = L * W
Plugging in the given values:
Abase = 14 inches * 8 inches
Abase = 112 square inches.
2. Calculating the perimeter of the base:
The perimeter of a rectangle is given by the formula 2(L+W), where L is the length and W is the width of the rectangle.
Perimeter of the base (P) = 2(L + W)
Plugging in the given values:
P = 2(14 inches + 8 inches)
P = 2(22 inches)
P = 44 inches.
3. Calculating the product of the perimeter of the base (P) and the height (H):
Ph = P * H
Plugging in the given values:
Ph = 44 inches * 10 inches
Ph = 440 square inches.
4. Calculating the surface area:
Surface Area = 2(Abase) + (Ph)
Surface Area = 2(112 square inches) + 440 square inches
Surface Area = 224 square inches + 440 square inches
Surface Area = 664 square inches.
Therefore, the surface area of the given prism is 664 in². Hence, the correct answer is O 664 in².