What is the surface area of a rectangular prism whose dimensions are 3 3/4 dm×4 1/2 dm×5 dm in square decimeters?(1 point)Responses116 1/4 dm2116 Start Fraction 1 over 4 End Fraction dm squared84 3/8 dm2 8/4 Start Fraction 3 over 8 End Fraction dm squared16 dm216 dm squared581/8 8 dm2
The surface area of a rectangular prism is given by the formula:
Surface Area = 2lw + 2lh + 2wh
where l = length, w = width, and h = height.
Given dimensions: l = 3 3/4 dm, w = 4 1/2 dm, h = 5 dm
Convert mixed fractions to improper fractions:
l = 3 3/4 = 15/4 dm
w = 4 1/2 = 9/2 dm
Substitute these values into the formula:
Surface Area = 2(15/4 x 9/2) + 2(15/4 x 5) + 2(9/2 x 5)
Surface Area = (45/2) + (75/2) + 45
Surface Area = 22.5 + 37.5 + 45
Surface Area = 105 square decimeters
Therefore, the surface area of the rectangular prism is 105 square decimeters.