Jaxon built a toy box in the shape of a rectangular prism with an open top. The diagram below shows the toy box and a net of the toy box.
TOY BOX
NET OF TOY BOX
14 ft
12 ft
15 ft
What is the surface area, in square feet, of the toy box?
To find the surface area of the rectangular prism toy box, we need to find the area of each of the six faces and then add them all together.
The toy box has 3 pairs of identical faces:
- The two 15 ft by 12 ft faces
- The two 14 ft by 12 ft faces
- The two 14 ft by 15 ft faces
The area of the 15 ft by 12 ft faces is 15 ft * 12 ft = 180 sq ft each, so both have an area of 180 sq ft * 2 = 360 sq ft
The area of the 14 ft by 12 ft faces is 14 ft * 12 ft = 168 sq ft each, so both have an area of 168 sq ft * 2 = 336 sq ft
The area of the 14 ft by 15 ft faces is 14 ft * 15 ft = 210 sq ft each, so both have an area of 210 sq ft * 2 = 420 sq ft
Adding all the areas together:
360 sq ft (15 ft by 12 ft faces) + 336 sq ft (14 ft by 12 ft faces) + 420 sq ft (14 ft by 15 ft faces) = 1116 sq ft
Therefore, the surface area of the toy box is 1116 square feet.