Find the lateral area and the surface area of the box to the nearest whole number
11 cm
1.57 cm
9 cm
Lateral area = perimeter of base x height
= (2 x 11 + 2 x 9) x 1.57
= 56.86 cm²
≈ 57 cm²
Surface area = 2 x area of base + lateral area
= 2 x 11 x 9 + 56.86
= 218.86 cm²
≈ 219 cm²
Therefore, the lateral area is 57 cm² and the surface area is 219 cm² (to the nearest whole number).
To find the lateral area of the box, we need to calculate the area of all four sides excluding the top and bottom.
The formula for the lateral area of a rectangular prism is:
Lateral Area = 2 * (length * height + width * height)
Given the dimensions of the box:
Length = 11 cm
Width = 1.57 cm
Height = 9 cm
Substituting the values into the formula, we get:
Lateral Area = 2 * (11 cm * 9 cm + 1.57 cm * 9 cm)
Lateral Area = 2 * (99 cm² + 14.13 cm²)
Lateral Area = 2 * 113.13 cm²
Lateral Area ≈ 226 cm² (rounded to the nearest whole number)
To find the surface area of the box, we need to calculate the area of all six sides.
The formula for the surface area of a rectangular prism is:
Surface Area = 2 * (length * width + length * height + width * height)
Substituting the values into the formula, we get:
Surface Area = 2 * (11 cm * 1.57 cm + 11 cm * 9 cm + 1.57 cm * 9 cm)
Surface Area = 2 * (17.27 cm² + 99 cm² + 14.13 cm²)
Surface Area = 2 * 130.4 cm²
Surface Area ≈ 260 cm² (rounded to the nearest whole number)
Therefore, the lateral area of the box is approximately 226 cm², and the surface area of the box is approximately 260 cm².