Question

1. mr. suarez wants to paint his storage shed. he needs to calculate the lateral surface area of the shed so that he will know how much paint to buy. the shed is in the shape of a rectangular prism with the dimensions shown below.

including the doors, what is the lateral surface area of the storage shed in square feet?
a. 622 square feet
b. 226 square feet
c. 384 square feet

Explanation:

Step1: Recall lateral surface area formula for rectangular prism

The lateral surface area (LSA) of a rectangular prism is given by the formula \( LSA = 2h(l + w) \), where \( l \) is the length, \( w \) is the width, and \( h \) is the height. From the diagram, we can identify the dimensions: length \( l = 17 \) ft, width \( w = 7 \) ft, and height \( h = 8 \) ft.

Step2: Substitute the values into the formula

First, calculate the sum of length and width: \( l + w = 17 + 7 = 24 \) ft.
Then, multiply by 2 and the height: \( LSA = 2\times8\times24 \).
First, calculate \( 2\times8 = 16 \), then \( 16\times24 = 384 \) square feet. Wait, but let's check again. Wait, maybe I mixed up the dimensions? Wait, the lateral surface area of a rectangular prism can also be calculated as the sum of the areas of the four lateral faces. The two faces with dimensions \( l \times h \) and two faces with dimensions \( w \times h \). So, area of two \( l \times h \) faces: \( 2\times l\times h = 2\times17\times8 = 272 \) square feet. Area of two \( w \times h \) faces: \( 2\times w\times h = 2\times7\times8 = 112 \) square feet. Then total lateral surface area is \( 272 + 112 = 384 \) square feet? Wait, but let's check the answer options. Option C is 384. Wait, but wait, maybe the diagram has different dimensions? Wait, the front face has length 17, depth 7, height 8. So lateral surface area: the sides are (17x8) two of them, and (7x8) two of them. So 2(178) + 2(78) = 2136 + 256 = 272 + 112 = 384. So that's correct. Wait, but let's check the options. Option C is 384. But wait, maybe I made a mistake? Wait, the problem says "including the doors". Wait, maybe the doors are part of the lateral surface? Wait, the lateral surface area of a rectangular prism is the area of the sides excluding the top and bottom. So the formula is correct. So the calculation gives 384. But wait, let's check the options again. Option C is 384. Wait, but let's recalculate:

\( 2\times(17\times8 + 7\times8) = 2\times(136 + 56) = 2\times192 = 384 \). Yes, that's correct.

Wait, but the options are A.622, B.226, C.384. So the correct answer is C? Wait, but maybe I misread the dimensions. Wait, the diagram: the length is 17, width is 7, height is 8. So yes, the lateral surface area is 384. So the correct option is C. Wait, but let's check again. Wait, maybe the height is different? Wait, the diagram shows 8 ft as the height (the side), 7 ft as the depth (the front to back), and 17 ft as the length (left to right). So yes, the lateral surface area is 2(lengthheight + widthheight) = 2(178 + 78) = 2(136 + 56) = 2192 = 384. So the answer is C.

Answer:

C. 384 square feet