Blanca is going to use a box that is a rectangular prism for a card box at her son’s birthday party. She will wrap and decorate the box. The dimensions of the box are shown in the diagram.
What is the total surface area of the box in square inches?
To calculate the total surface area of the box, we need to find the area of each of its six faces and then add them together.
The front and back faces have dimensions 5 inches by 4 inches, so each of these faces has an area of (5 inches)(4 inches) = 20 square inches.
The top and bottom faces have dimensions 6 inches by 5 inches, so each of these faces has an area of (6 inches)(5 inches) = 30 square inches.
The left and right faces have dimensions 6 inches by 4 inches, so each of these faces has an area of (6 inches)(4 inches) = 24 square inches.
Adding up all the face areas, we have:
Front and back faces: 20 square inches each
Top and bottom faces: 30 square inches each
Left and right faces: 24 square inches each
Total surface area = (20 + 20) + (30 + 30) + (24 + 24) = 40 + 60 + 48 = 148 square inches.
Therefore, the total surface area of the box is 148 square inches.
Micah is going to paint his woodworking shop. The shop is a rectangular prism. The dimensions of the shop are shown in the diagram.
Including the doors, what is the lateral surface area of the shop in square feet?
The lateral surface area of a rectangular prism is the sum of the areas of its four lateral faces. The lateral faces are the faces that are not the top or bottom faces.
From the diagram, the dimensions of the shop are labeled as follows:
Length (l) = 15 feet
Width (w) = 10 feet
Height (h) = 8 feet
The four lateral faces are the front, back, left, and right faces.
The front and back faces have dimensions 15 feet by 8 feet, so each of these faces has an area of (15 feet)(8 feet) = 120 square feet.
The left and right faces have dimensions 10 feet by 8 feet, so each of these faces has an area of (10 feet)(8 feet) = 80 square feet.
Adding up all the face areas, we have:
Front and back faces: 120 square feet each
Left and right faces: 80 square feet each
Lateral surface area = (120 + 120) + (80 + 80) = 240 + 160 = 400 square feet.
Therefore, the lateral surface area of the shop, including the doors, is 400 square feet.
Micah is going to paint his woodworking shop. The shop is a rectangular prism. The dimensions of the shop are shown in the diagram.
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