Question
what is the total surface area of the figure
15 in 12 in 7 in 6 in 6 in 6 in 4 in 4 in
15 in 12 in 7 in 6 in 6 in 6 in 4 in 4 in
Answers
GPT 3.5
To find the total surface area of the figure, we need to find the surface area of each individual shape and then add them up.
The figure consists of:
- A rectangular prism with dimensions 15 in x 12 in x 7 in: Surface area = 2lw + 2lh + 2wh = 2(15)(12) + 2(15)(7) + 2(12)(7) = 360 + 210 + 168 = 738 square inches
- Two rectangular prisms with dimensions 6 in x 6 in x 4 in: Surface area for each prism = 2lw + 2lh + 2wh = 2(6)(6) + 2(6)(4) + 2(6)(4) = 72 + 48 + 48 = 168 square inches (for each prism)
- Two cubes with side length 4 in: Surface area for each cube = 6s^2 = 6(4)^2 = 6(16) = 96 square inches (for each cube)
Adding up the surface areas of all the shapes:
738 + 2(168) + 2(96) = 738 + 336 + 192 = 1266 square inches
So, the total surface area of the figure is 1266 square inches.
The figure consists of:
- A rectangular prism with dimensions 15 in x 12 in x 7 in: Surface area = 2lw + 2lh + 2wh = 2(15)(12) + 2(15)(7) + 2(12)(7) = 360 + 210 + 168 = 738 square inches
- Two rectangular prisms with dimensions 6 in x 6 in x 4 in: Surface area for each prism = 2lw + 2lh + 2wh = 2(6)(6) + 2(6)(4) + 2(6)(4) = 72 + 48 + 48 = 168 square inches (for each prism)
- Two cubes with side length 4 in: Surface area for each cube = 6s^2 = 6(4)^2 = 6(16) = 96 square inches (for each cube)
Adding up the surface areas of all the shapes:
738 + 2(168) + 2(96) = 738 + 336 + 192 = 1266 square inches
So, the total surface area of the figure is 1266 square inches.