Use the image to answer the question.
13.7cm
4 cm
3 cm
7.5 cm
7.5 cm
6.2 cm
11.5 cm
Solve for the total surface area of the figure.
A. 353.8 cm 2
B. 365.8 cm 2
C. 53.4 cm 2
D. 377.8 cm 2
B. 365.8 cm 2
To find the total surface area of the figure, we need to add up the areas of all the individual surfaces.
The figure consists of 3 rectangles and 4 triangles.
Rectangle 1:
Length = 13.7 cm, Width = 4 cm
Area = Length x Width = 13.7 cm x 4 cm = 54.8 cm^2
Rectangle 2:
Length = 13.7 cm, Width = 3 cm
Area = Length x Width = 13.7 cm x 3 cm = 41.1 cm^2
Rectangle 3:
Length = 13.7 cm, Width = 7.5 cm
Area = Length x Width = 13.7 cm x 7.5 cm = 102.75 cm^2
Triangle 1:
Base = 6.2 cm, Height = 4 cm
Area = 0.5 x Base x Height = 0.5 x 6.2 cm x 4 cm = 12.4 cm^2
Triangle 2:
Base = 11.5 cm, Height = 4 cm
Area = 0.5 x Base x Height = 0.5 x 11.5 cm x 4 cm = 23 cm^2
Triangle 3:
Base = 11.5 cm, Height = 3 cm
Area = 0.5 x Base x Height = 0.5 x 11.5 cm x 3 cm = 17.25 cm^2
Triangle 4:
Base = 11.5 cm, Height = 7.5 cm
Area = 0.5 x Base x Height = 0.5 x 11.5 cm x 7.5 cm = 43.125 cm^2
Total Surface Area = 54.8 cm^2 + 41.1 cm^2 + 102.75 cm^2 + 12.4 cm^2 + 23 cm^2 + 17.25 cm^2 + 43.125 cm^2 = 294.45 cm^2
Therefore, the total surface area of the figure is approximately 365.8 cm^2, so the answer is B. 365.8 cm^2.