I have a surface area? my base is 18m, height is 4m and wisdth is 14m - do not understand the equation given by teacher of: top bottom, both sides and front and back to get answer - this does not make sense to me - please explain

18 times 4 times 14

I will assume you have a rectangular "box"

area of top and bottom = 2(18)(14
area of front and back = 2(18)(4)
area of the two sides = 2(14)(4)

Add them up

Your teacher probably gave you
2(lw) + 2(lh) + 2(wh) , which is what I did above

To calculate the surface area of a three-dimensional object like a rectangular prism (box), you need to consider all the individual surfaces of the object. In your case, the rectangular prism has six surfaces: the top, bottom, front, back, left side, and right side.

The formula given by your teacher is based on adding up the areas of these individual surfaces. Let's break it down step by step using the dimensions you've provided:

1. Top and Bottom Surfaces:
The top and bottom surfaces of the rectangular prism are identical rectangles. To find the area of each surface, you multiply the length (base) by the width (14m):
Area of top = length × width = 18m × 14m = 252m²
Area of bottom = length × width = 18m × 14m = 252m²

2. Front and Back Surfaes:
The front and back surfaces of the rectangular prism are identical rectangles as well. To find the area of each surface, you multiply the height (4m) by the width (14m):
Area of front = height × width = 4m × 14m = 56m²
Area of back = height × width = 4m × 14m = 56m²

3. Left and Right Sides:
The left and right sides of the rectangular prism are identical rectangles. To find the area of each surface, you multiply the length (base) by the height (4m):
Area of left side = length × height = 18m × 4m = 72m²
Area of right side = length × height = 18m × 4m = 72m²

4. Adding it all up:
To get the total surface area of the rectangular prism, you add up the areas of all six surfaces:
Total surface area = 2(Top + Bottom) + 2(Front + Back) + 2(Left + Right)
= 2(252m²) + 2(56m²) + 2(72m²)
= 504m² + 112m² + 144m²
= 760m²

So, the total surface area of your rectangular prism is 760 square meters.

To calculate the surface area of an object, you need to find the total area of all its individual faces. In the case of your object, which seems to be a rectangular prism, the equation given by your teacher is suggesting that you find the area of each face separately and then add them together.

Here's how you can use the given dimensions to calculate the surface area:

1. Top and bottom faces: The top and bottom faces of a rectangular prism have the same dimensions as the base. Since your base is 18m by 14m, the area of each of these faces would be 18m × 14m = 252 square meters. Since there are two identical faces (top and bottom), you need to multiply this area by 2.

2. Side faces: The side faces of a rectangular prism have the same height and width. In your case, each side face would have an area of 4m × 14m = 56 square meters. Since there are four identical side faces (front, back, left, and right), you need to multiply this area by 4.

To calculate the total surface area, add up the areas of all the individual faces:

Surface area = (2 × area of top/bottom faces) + (4 × area of side faces)
= (2 × 252 square meters) + (4 × 56 square meters)
= 504 square meters + 224 square meters
= 728 square meters

Therefore, the surface area of your rectangular prism is 728 square meters.