Question

Solve for the total surface area of the figure. There are 2 3D composite figures stacked on top of each other. It is a rectangular prism stacked on a smaller rectangular prism . The dimensions of the rectangular prism are= 13.7cm for length, 4 for height, 3 for width. The dimensions for the smaller rectangular prism are= 6.2cm for length, 3 for width, 7.5 for height. Please find the surface area and remeber to subrtract the hidden area since these shapes are stacked up on eachother

Answer 1

First, let's find the surface area of each individual rectangular prism.

Surface area of the larger rectangular prism:
- Front and back faces: 2(13.7cm x 4cm) = 54.8cm^2
- Top and bottom faces: 2(13.7cm x 3cm) = 82.2cm^2
- Side faces: 2(4cm x 3cm) = 24cm^2

Total surface area of the larger rectangular prism = 54.8cm^2 + 82.2cm^2 + 24cm^2 = 161cm^2

Surface area of the smaller rectangular prism:
- Front and back faces: 2(6.2cm x 3cm) = 37.2cm^2
- Top and bottom faces: 2(6.2cm x 7.5cm) = 93cm^2
- Side faces: 2(3cm x 7.5cm) = 45cm^2

Total surface area of the smaller rectangular prism = 37.2cm^2 + 93cm^2 + 45cm^2 = 175.2cm^2

Next, calculate the total surface area of the composite figure by adding the surface area of both rectangular prisms and subtracting the areas that are hidden:

Total surface area = (161cm^2 + 175.2cm^2) - (13.7cm x 3cm) = 336.2cm^2 - 41.1cm^2 = 295.1cm^2

So, the total surface area of the 3D composite figure when stacked on top of each other is 295.1 square centimeters.