ABC Elementary wants to purchase new computers for their school. They are curious how the new laptops compare to their current ones in terms of space as their enrollment numbers are increasing and space is not. What would the surface area be if the length is 13 inches, the width is 7.5 inches, and the height is 7.5 inches? The triangle’s hypotenuse is 10.61 inches. (Remember the hypotenuse is the longest side of the triangle.) Round your answer to the nearest hundredth if necessary.
To find the surface area of the laptop, we need to calculate the areas of the two rectangles formed by the length and width, the length and height, and the width and height, and then add them together.
Area of rectangle formed by length and width:
Area = length x width
Area = 13 inches x 7.5 inches
Area = 97.5 square inches
Area of rectangle formed by length and height:
Area = length x height
Area = 13 inches x 7.5 inches
Area = 97.5 square inches
Area of rectangle formed by width and height:
Area = width x height
Area = 7.5 inches x 7.5 inches
Area = 56.25 square inches
Now we add up the areas of the three rectangles to find the total surface area of the laptop:
Total Surface Area = 97.5 square inches + 97.5 square inches + 56.25 square inches
Total Surface Area = 251.25 square inches
Therefore, the surface area of the laptop with dimensions 13 inches x 7.5 inches x 7.5 inches is 251.25 square inches.
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To find the surface area of the laptop, we need to calculate the areas of the six sides (four rectangular sides and two triangular sides).
Area of rectangular sides:
Top and bottom sides = length x width = 13 inches x 7.5 inches = 97.5 square inches x 2 sides = 195 square inches
Front and back sides = length x height = 13 inches x 7.5 inches = 97.5 square inches x 2 sides = 195 square inches
Left and right sides = width x height = 7.5 inches x 7.5 inches = 56.25 square inches x 2 sides = 112.5 square inches
Area of triangular sides:
Each triangular side = (1/2) * base * height = (1/2) * 7.5 inches * 10.61 inches = 39.8035 square inches x 2 sides = 79.607 square inches
Total Surface Area = 195 square inches + 195 square inches + 112.5 square inches + 79.607 square inches
Total Surface Area = 582.107 square inches
Therefore, the surface area of the laptop with dimensions 13 inches x 7.5 inches x 7.5 inches is 582.107 square inches.