Answer: Ray will need approximately 40 square inches of decorative paper to cover the lateral area of his paperweight. Rounded to the nearest square inch, he will need 40 square inches.
Explanation:
To find the lateral area of the rectangular pyramid, we need to find the area of each triangular face and add them up.
Let's label the dimensions of the rectangular pyramid:
The base of the rectangular pyramid has dimensions 4 inches by 6 inches.
The height of the rectangular pyramid is 3 inches.
First, we need to find the slant height of the pyramid, which is the hypotenuse of each triangular face. We can use the Pythagorean theorem to find it:
slant height = √( (1.5)^2 + 3^2 ) = √( 2.25 + 9 ) = √11.25 ≈ 3.354
Now we can find the area of each triangular face using the formula:
area = 0.5 x base x height
The base of each triangular face is the width of the rectangular base, which is 6 inches. The height of each triangular face is the slant height we just found, which is approximately 3.354 inches.
So, the area of each triangular face is:
area = 0.5 x 6 x 3.354 = 10.062 square inches (rounded to three decimal places)
There are four triangular faces, so the total lateral area of the pyramid is:
total lateral area = 4 x 10.062 = 40.248 square inches (rounded to three decimal places)
Therefore, Ray will need approximately 40 square inches of decorative paper to cover the lateral area of his paperweight. Rounded to the nearest square inch, he will need 40 square inches.