The figure below is a net for a rectangular prism. Side a = 23 inches, side b = 17 inches, and side c = 8 inches. What is the surface area of this figure?
There are six faces to a rectangular prism, each with an area that can be calculated by multiplying the length and width of the face.
Face 1: a x b = 23 x 17 = 391 square inches
Face 2: a x b = 23 x 17 = 391 square inches
Face 3: c x b = 8 x 17 = 136 square inches
Face 4: c x b = 8 x 17 = 136 square inches
Face 5: a x c = 23 x 8 = 184 square inches
Face 6: a x c = 23 x 8 = 184 square inches
To find the total surface area of the rectangular prism, we add up the areas of all six faces:
391 + 391 + 136 + 136 + 184 + 184 = 1,422 square inches
Therefore, the surface area of the rectangular prism is 1,422 square inches.
To find the surface area of a rectangular prism, we need to find the area of each of the six faces and then sum them up.
The rectangular prism has six faces: two identical rectangular faces with dimensions 23 inches by 17 inches, two identical rectangular faces with dimensions 23 inches by 8 inches, and two identical rectangular faces with dimensions 17 inches by 8 inches.
To find the area of each face, we use the formula: Area = length x width.
Face 1: Area = 23 inches x 17 inches = 391 square inches
Face 2: Area = 23 inches x 17 inches = 391 square inches
Face 3: Area = 23 inches x 8 inches = 184 square inches
Face 4: Area = 23 inches x 8 inches = 184 square inches
Face 5: Area = 17 inches x 8 inches = 136 square inches
Face 6: Area = 17 inches x 8 inches = 136 square inches
Now we sum up the areas of all the faces:
391 square inches + 391 square inches + 184 square inches + 184 square inches + 136 square inches + 136 square inches = 1422 square inches.
Therefore, the surface area of this rectangular prism is 1422 square inches.