Leigh Ann is designing a wrapper for a new dark chocolate candy bar that her company is going to sell The candy bar is a triangular prism . The dimensions of the candy bar are shown in the diagram 7.4 cm 6.9 cm 7.4 cm 9.9 cm 5.1 cm Which measurement is closest to the total surface area of the candy bar in square contimeters ?
To find the total surface area of the candy bar, we need to find the sum of the areas of all of its faces.
The candy bar is a triangular prism, so it has 2 triangular faces and 3 rectangular faces.
The area of a triangular face can be calculated using the formula:
Area of a triangle = 1/2 × base × height.
The area of a rectangular face can be calculated using the formula:
Area of a rectangle = length × width.
Given the dimensions of the candy bar:
Triangular face 1:
base = 7.4 cm
height = 9.9 cm
Area of triangular face 1 = 1/2 × 7.4 cm × 9.9 cm = 36.63 cm^2 (rounded to 2 decimal places).
Triangular face 2:
base = 6.9 cm
height = 5.1 cm
Area of triangular face 2 = 1/2 × 6.9 cm × 5.1 cm = 17.65 cm^2 (rounded to 2 decimal places).
Rectangular face 1:
length = 7.4 cm
width = 9.9 cm
Area of rectangular face 1 = 7.4 cm × 9.9 cm = 73.26 cm^2 (rounded to 2 decimal places).
Rectangular face 2:
length = 6.9 cm
width = 5.1 cm
Area of rectangular face 2 = 6.9 cm × 5.1 cm = 35.19 cm^2 (rounded to 2 decimal places).
Rectangular face 3:
length = 7.4 cm
width = 6.9 cm
Area of rectangular face 3 = 7.4 cm × 6.9 cm = 51.06 cm^2 (rounded to 2 decimal places).
Now, we can calculate the total surface area by summing the areas of all the faces:
Total surface area = Area of triangular face 1 + Area of triangular face 2 + Area of rectangular face 1 + Area of rectangular face 2 + Area of rectangular face 3
= 36.63 cm^2 + 17.65 cm^2 + 73.26 cm^2 + 35.19 cm^2 + 51.06 cm^2
= 213.79 cm^2.
Therefore, the measurement closest to the total surface area of the candy bar is 213.79 cm^2.