8 ft 20 ft 15ft 8ft 8ft 12ft
What is the surface area of the figure?
To calculate the surface area of the figure, we need to first break it down into individual shapes and then calculate the surface area of each shape separately.
1. The figure consists of two rectangular prisms and one triangular prism.
Surface area of rectangular prism = 2(lw + lh + wh)
Surface area of triangular prism = (base perimeter x height) + (base area)
Surface area of figure = Surface area of first rectangular prism + Surface area of second rectangular prism + Surface area of triangular prism
Calculating for the surface area of each shape:
Rectangular prism 1:
Surface area = 2(8)(20 + 8 + 20) = 2(8)(48) = 768 ft^2
Rectangular prism 2:
Surface area = 2(15)(8 + 8 + 15) = 2(15)(31) = 930 ft^2
Triangular prism:
Base perimeter = 8 + 8 + 12 = 28 ft
Base area = 1/2 * base * height = 1/2 * 28 * 8 = 112 ft^2
Surface area = (28)(8) + (112) = 224 + 112 = 336 ft^2
Now, add the surface areas of each shape together to find the total surface area of the figure:
Total surface area = 768 + 930 + 336 = 2034 ft^2
Therefore, the surface area of the figure is 2034 square feet.