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
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.