Micah is going to paint his woodworking shop. The shop is a rectangular prism. The dimensions of the shop are shown in the diagram.
Height= 9 ft.
Width= 7.9 ft.
Length= 15.8 ft.
Including the doors, what is the lateral surface area of the shop in square feet?
Responses
A 676.24 ft2676.24 ft 2
B 213.3 ft2213.3 ft 2
C 426.6 ft2426.6 ft 2
D 1,123.38 ft2
To find the lateral surface area of the shop, we need to find the area of each side of the rectangular prism except for the top and bottom. The formula for the lateral surface area of a rectangular prism is 2 * (length * height + width * height).
Using the given dimensions:
Lateral surface area = 2 * (15.8 ft * 9 ft + 7.9 ft * 9 ft)
Lateral surface area = 2 * (142.2 ft^2 + 71.1 ft^2)
Lateral surface area = 2 * 213.3 ft^2
Lateral surface area = 426.6 ft^2
So the lateral surface area of the shop, including the doors, is 426.6 ft^2.
Therefore, the correct answer is C) 426.6 ft^2.
A pencil holder shaped like a triangular prism is shown.
Height= 12 cm.
Width= 7 cm.
Length= 10 cm.
What is the lateral surface area of the pencil holder in square centimeters?
To find the lateral surface area of the triangular prism pencil holder, we need to find the area of each side of the prism except for the bases. The formula for the lateral surface area of a triangular prism is (perimeter of the base) * height.
First, let's find the perimeter of the base. Since the pencil holder is shaped like a triangular prism, the base is a triangle.
The perimeter of a triangle is found by adding up the lengths of all three sides.
Using the given dimensions:
We have a triangle with sides of length 7 cm, 10 cm, and 10 cm (since the length and width of the pencil holder are the same).
The perimeter of the base = 7 cm + 10 cm + 10 cm = 27 cm.
Now, we can find the lateral surface area by multiplying the perimeter of the base by the height:
Lateral surface area = 27 cm * 12 cm
Lateral surface area = 324 cm^2.
Therefore, the lateral surface area of the pencil holder is 324 square centimeters.
Leigh Ann is designing a wrapper for a new dark chocolate candy bar that her company is going to sell. The candy bar is a triangular prism. The dimensions of the candy bar are shown in the diagram.
Height= 7.4 cm.
Width= 9.9 cm.
Length= 5.1 cm.
Which measurement is closest to the total surface area of the candy bar in square centimeters?
Responses
A 232.20 cm2232.20 cm 2
B 197.01 cm2197.01 cm 2
C 265.32 cm2265.32 cm 2
D 174.19 cm2
To find the total surface area of the triangular prism candy bar, we need to find the area of each face and add them together.
The triangular faces will have the formula (base * height) / 2, and the rectangular faces will have the formula (length * width).
First, let's find the area of the triangular faces.
Since the candy bar is a triangular prism, we have two triangular faces, one on each end.
Using the given dimensions:
Area of the triangular faces = (9.9 cm * 7.4 cm) / 2 * 2
Area of the triangular faces = 72.9 cm^2
Next, let's find the area of the rectangular faces.
Since the candy bar is a triangular prism, we have three rectangular faces, one for each side.
Using the given dimensions:
Area of the rectangular faces = (5.1 cm * 7.4 cm) * 3
Area of the rectangular faces = 112.86 cm^2
Now, let's add up the areas of all the faces to find the total surface area:
Total surface area = area of triangular faces + area of rectangular faces
Total surface area = 72.9 cm^2 + 112.86 cm^2
Total surface area = 185.76 cm^2
Therefore, the total surface area of the candy bar is closest to 185.76 square centimeters.
So the closest measurement to the total surface area of the candy bar is B) 197.01 cm^2.