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
6.9cm 7.4cm 5.1cm 9.9cm 7.4cm
Which measurement is closest to the total surface area of the candy bar in square centimeters?
A 232.20 cm2
B 197.01 cm2
C 265.32 cm2
D 174.19 cm2
To find the total surface area of the triangular prism, we need to find the areas of all the individual faces and then sum them up.
The triangular faces of the prism have base and height dimensions given as 9.9 cm and 7.4 cm respectively. So, the area of each triangular face is:
(1/2) * base * height = (1/2) * 9.9 cm * 7.4 cm = 36.63 cm^2 (rounded to two decimal places)
As there are two triangular faces on the prism, their combined area is 2 * 36.63 cm^2 = 73.26 cm^2.
The rectangular faces have dimensions of 6.9 cm, 7.4 cm, and 5.1 cm. So, the total area of the two rectangular faces is:
2 * (6.9 cm * 7.4 cm + 6.9 cm * 5.1 cm + 7.4 cm * 5.1 cm)
= 2 * (51.06 cm^2 + 35.19 cm^2 + 37.74 cm^2)
= 2 * 123.99 cm^2
= 247.98 cm^2
Finally, we add the areas of the triangular faces and the rectangular faces to find the total surface area of the prism:
Total surface area = 73.26 cm^2 + 247.98 cm^2 = 321.24 cm^2 (rounded to two decimal places)
Therefore, the measurement closest to the total surface area of the candy bar is C) 265.32 cm^2.
are you sure?
Apologies for the incorrect calculation. Let's recalculate the total surface area.
The triangular faces of the prism have base and height dimensions given as 9.9 cm and 7.4 cm respectively. So, the area of each triangular face is:
(1/2) * base * height = (1/2) * 9.9 cm * 7.4 cm = 36.63 cm^2 (rounded to two decimal places)
As there are two triangular faces on the prism, their combined area is 2 * 36.63 cm^2 = 73.26 cm^2.
The rectangular faces have dimensions of 6.9 cm, 7.4 cm, and 5.1 cm. So, the total area of the two rectangular faces is:
2 * (6.9 cm * 7.4 cm + 7.4 cm * 5.1 cm)
= 2 * (51.06 cm^2 + 37.74 cm^2)
= 2 * 88.80 cm^2
= 177.60 cm^2
Finally, we add the areas of the triangular faces and the rectangular faces to find the total surface area of the prism:
Total surface area = 73.26 cm^2 + 177.60 cm^2 = 250.86 cm^2 (rounded to two decimal places)
Therefore, the measurement closest to the total surface area of the candy bar is C) 265.32 cm^2.