Question

If a rectangular prism with a length of 12 feet and a width of 9 feet has a surface area of 930 square feet find its height

Answer 1

Height is 17 ft.

Explanation:

Given: Rectangular Prism is also called cuboid

Length, L = 12 ft. and width, W = 9 ft.

Surface Area of cuboid, SA = 930 ft.²

To find: height , H

The surface area of a rectangular prism or cuboid

SA = 2(LW +WH + LH)

930 = 2(12×9 +9H + 12H)

`(930)/(2)=108 +9H + 12H`

465 = 108 + 9H + 12H

108 + 9H + 12H = 465

21H + 108 = 465

21H = 465 - 108

21H = 357

`H=\farc{357}{21}`

H = 17

therefore, Height is 17 ft.

Answer 2

The height is 17 ft

Explanation:

The surface area of a rectangular prism is

SA = 2(LW +WH + LH)

where L = length, W = width, and H = height

We know SA = 930, L = 12, and W = 9

930 = 2(12*9 +9H + 12H)

Divide each side by 2

930/2 = 2/2(12*9 +9H + 12H)

465 = (12*9 +9H + 12H)

Combine like terms

465 = 84+21H

Subtract 84 from each side

465-84 = 84-84+21H

357 = 21H

Divide by 21

357/21=21H/21

17 = H

The height is 17 ft