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.
To find the surface area of the laptop, we need to find the area of each of its six sides and then add them together.
First, we can use the Pythagorean theorem to find the length of the third side of the triangle formed by the height and width of the laptop:
a^2 + b^2 = c^2
7.5^2 + 7.5^2 = c^2
56.25 + 56.25 = c^2
112.5 = c^2
c ≈ 10.61
Now we can find the area of each side:
- Top and bottom: length x width = 13 x 7.5 = 97.5
- Front and back: height x width = 7.5 x 7.5 = 56.25
- Sides: height x length = 7.5 x 13 = 97.5
To find the total surface area, we add these together:
97.5 + 97.5 + 56.25 + 56.25 + 97.5 + 97.5 = 502.5
Therefore, the surface area of the laptop is approximately 502.5 square inches.