Solve for the surface area of the rectangular prism.

Question

12in 5in 3in

Answer 1

To find the surface area of a rectangular prism, you need to calculate the area of each of the six faces and then add them all together.

The formula for the surface area of a rectangular prism is:
Surface Area = 2lw + 2lh + 2wh

Given:
Length (l) = 12 inches
Width (w) = 5 inches
Height (h) = 3 inches

Calculating the area of each face:
1. Front and back faces: 2lw
Front face area = 2(12)(3) = 72 square inches
Back face area = 2(12)(3) = 72 square inches

2. Top and bottom faces: 2wh
Top face area = 2(5)(3) = 30 square inches
Bottom face area = 2(5)(3) = 30 square inches

3. Right and left faces: 2lh
Right face area = 2(12)(5) = 120 square inches
Left face area = 2(12)(5) = 120 square inches

Adding all face areas together:
Surface Area = Front face area + Back face area + Top face area + Bottom face area + Right face area + Left face area
Surface Area = 72 + 72 + 30 + 30 + 120 + 120
Surface Area = 444 square inches

Therefore, the surface area of the rectangular prism is 444 square inches.