What is the total surface area of the figure 10 mm, 16 mm, 8 mm, 6 mm, 6 mm, 2 mm???

Question

____, mm^2

Answer 1

To find the total surface area of this figure, we first need to determine the surface area of each individual shape and then sum them up.

The figure consists of a rectangular prism (10mm x 16mm x 8mm), a rectangular pyramid (base 6mm x 6mm, height 2mm), and another rectangular prism (6mm x 6mm x 2mm).

1. Rectangular Prism: Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(10)(16) + 2(10)(8) + 2(16)(8)
Surface Area = 320 + 160 + 256 = 736 mm^2

2. Rectangular Pyramid: Surface Area = Base Area + 1/2(pl)
Base Area = 6 * 6 = 36 mm^2
Surface Area = 36 + 1/2(6*2) + 1/2(6*2) + 1/2(6*6) = 36 + 6 + 6 + 18 = 66 mm^2

3. Second Rectangular Prism: Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(6)(6) + 2(6)(2) + 2(6)(2)
Surface Area = 72 + 24 + 24 = 120 mm^2

Total Surface Area = 736 + 66 + 120 = 922 mm^2

Therefore, the total surface area of the figure is 922 mm^2.

Answer 2

wrong

Answer 3

Apologies for the mistake. Let's re-calculate the surface area of the figure with the given dimensions.

The figure consists of:
- Rectangular prism with dimensions 10mm x 16mm x 8mm
- Rectangular pyramid with base dimensions 6mm x 6mm and height 2mm
- Rectangular prism with dimensions 6mm x 6mm x 2mm

The total surface area is the sum of the surface areas of each individual shape.

1. Surface area of rectangular prism:
Surface Area = 2(lw + lh + wh)
Surface Area = 2(10*16 + 10*8 + 16*8)
Surface Area = 2(160 + 80 + 128)
Surface Area = 2(368)
Surface Area = 736 mm^2

2. Surface area of rectangular pyramid:
The surface area of a rectangular pyramid is calculated as: Base Area + (1/2)*perimeter of base*slant height
Base Area = 6*6 = 36 mm^2
Slant height = sqrt(2^2 + 6^2) = sqrt(40) = 2sqrt(10)
Perimeter = 4*6 = 24
Surface Area = 36 + (1/2)*24*(2sqrt(10))
Surface Area = 36 + 24*sqrt(10)
Surface Area ≈ 109.471 mm^2

3. Surface area of the second rectangular prism:
Surface Area = 2(lw + lh + wh)
Surface Area = 2(6*6 + 6*2 + 6*2)
Surface Area = 2(36 + 12 + 12)
Surface Area = 2(60)
Surface Area = 120 mm^2

Total Surface Area = 736 + 109.471 + 120
Total Surface Area ≈ 965.471 mm^2

Therefore, the correct total surface area of the figure is approximately 965.471 mm^2. Thank you for your patience.

Answer 4

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Answer 5

Apologies for the confusion. Let's re-calculate the total surface area of the figure:

Given dimensions:
- Rectangular prism: 10 mm x 16 mm x 8 mm
- Rectangular pyramid: base 6 mm x 6 mm, height 2 mm
- Rectangular prism: 6 mm x 6 mm x 2 mm

1. Surface area of the rectangular prism:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(10*16 + 10*8 + 16*8)
Surface Area = 2(160 + 80 + 128)
Surface Area = 2(368)
Surface Area = 736 mm^2

2. Surface area of the rectangular pyramid:
Base Area = 6*6 = 36 mm^2
Lateral Area = 1/2 * Perimeter of base * Slant height
Perimeter of base = 4*6 = 24
Slant height = sqrt(6^2 + 2^2) = sqrt(40) = 2sqrt(10)
Lateral Area ≈ 1/2 * 24 * 2sqrt(10) = 24sqrt(10) mm^2
Total Surface Area of the pyramid = Base Area + Lateral Area
Total Surface Area = 36 + 24sqrt(10) ≈ 76.972 mm^2

3. Surface area of the second rectangular prism:
Surface Area = 2lw + 2lh + 2wh
Surface Area = 2(6*6 + 6*2 + 6*2)
Surface Area = 2(36 + 12 + 12)
Surface Area = 2(60)
Surface Area = 120 mm^2

Total Surface Area = 736 + 76.972 + 120
Total Surface Area ≈ 932.972 mm^2

Therefore, the correct total surface area of the figure is approximately 932.972 mm^2. Thank you for your patience.