Fran bought a box of cookies that matches the dimensions of the solid below. How many square units of cardboard were used to construct the box? If your solution is not a whole number, round to the nearest tenth. width=4mm length=3mm height=5.7mm height=4mm
To calculate the surface area of the box, we need to find the area of each of the six faces and add them together.
1. Top and bottom faces:
- Each of these faces has a length of 4 mm and width of 3 mm. So, the area of each is 4 mm * 3 mm = 12 square mm.
2. Front and back faces:
- Each of these faces has a length of 5.7 mm and width of 3 mm. So, the area of each is 5.7 mm * 3 mm = 17.1 square mm.
3. Left and right faces:
- Each of these faces has a length of 5.7 mm and height of 4 mm. So, the area of each is 5.7 mm * 4 mm = 22.8 square mm.
Now, add all the areas together to find the total surface area of the box:
Total surface area = 2(12) + 2(17.1) + 2(22.8)
Total surface area = 24 + 34.2 + 45.6
Total surface area = 103.8 square mm
Therefore, the box used approximately 103.8 square mm of cardboard to construct. Rounding to the nearest tenth, we get 103.8 square mm.