"An office building is in the shape of a right rectangular prism wit height 200m, length 60m and width 40m. The top quarter of each vertical face of the building is to be covered with a large banner. What is the total surface area to be covered with banners?"

I don't know what they mean by "top quarter of each vertical face" and therefore don't know where to start. I have sketched the triangle and its dimensions.

If it is a rectangular prism, why would you sketch a triangle?

First, find the perimeter, 2L + 2W. Then multiply by 200/4, "the top quarter of each vertical face."

To understand what is meant by the "top quarter of each vertical face," let's break down the problem step by step:

1. Visualize the building: Draw a rectangular prism with dimensions given - height of 200m, length of 60m, and width of 40m.

2. Identify the vertical faces: A rectangular prism has 6 faces. In this case, we need to focus on the four vertical faces of the building without including the top and bottom faces.

3. Divide the vertical faces: Each vertical face is divided into four equal parts. From the top, we need to cover the top quarter, from the top down to one-fourth of the height.

4. Calculate the area of each vertical face: The area of each vertical face is the length multiplied by the width, which is 60m x 40m = 2400 square meters.

5. Calculate the area to be covered with banners on each vertical face: As we need to cover the top quarter of each vertical face, we only consider one-fourth of the area calculated in step 4. So, the area to be covered on each vertical face is 1/4 x 2400 = 600 square meters.

6. Calculate the total surface area to be covered with banners: As there are 4 vertical faces, we need to multiply the area covered on each face by the number of faces. Therefore, the total surface area to be covered with banners is 4 x 600 = 2400 square meters.

So, the total surface area to be covered with banners is 2400 square meters.

To understand what they mean by the "top quarter of each vertical face," let's break it down step by step.

First, visualize the shape of the building—a right rectangular prism. This means it looks like a rectangular box with six faces: the top and bottom faces are rectangles, while the remaining four faces are vertical rectangles.

Now, focus on the vertical faces. Since each face is a rectangle, we can distinguish between the shorter sides (width) and the longer sides (height). In this case, the width of each vertical face is 40m, while the height is 200m.

The phrase "top quarter of each vertical face" means that only the top 1/4th portion of each vertical face will be covered with a banner. To calculate this, we need to find the height of the covered portion.

Since the height of the entire vertical face is 200m, to find the height of the covered portion, we can apply the formula:

Height of the covered portion = 1/4 * Height of the vertical face

Therefore, the height of the covered portion = 1/4 * 200m = 50m.

Now that we know the dimensions of the covered portion (50m height and 40m width), we can calculate the surface area of a single covered portion using the formula:

Surface area of a rectangle = Length * Width

In this case, the length of the covered portion is equal to the width of the original vertical face, which is 40m.

So, the surface area of a single covered portion = 40m * 50m = 2000m².

Since we have four vertical faces, the total surface area to be covered with banners is:

Total surface area = Surface area of a single covered portion * Number of vertical faces

Total surface area = 2000m² * 4 = 8000m².

Therefore, the total surface area to be covered with banners is 8000m².