Question

Yusuf wraps a gift box in the shape of a triangular pyramid. The figure below shows a net for the gift box.On the tactile printout of the following graphs, x is 1010 feet and y is 8, point, 6, 68.66 feet. 10 ft 8.66 ft An image is shown. To download tactile, press SHIFT-CONTROL-U for UEB or SHIFT-CONTROL-N for Nemeth. If all the triangles are equilateral, how much wrapping paper did he use, in square feet?

Answer 1

[AI-generated answer — Bot GPT 3.5]

To calculate the total amount of wrapping paper used, we need to find the surface area of the triangular pyramid.

First, we need to determine the side length of the equilateral triangle. Since the height of the pyramid is given as 8 feet, and the height of an equilateral triangle bisects the base at a 90-degree angle, we can use the Pythagorean theorem to find the side length of the triangle.

Let's call the side length of the equilateral triangle s. Using the height of 8 feet and half of the base of 10 feet (which would be 5 feet), we have:

s^2 = 5^2 + 8^2
s^2 = 25 + 64
s^2 = 89
s ≈ 9.43 feet

Now, we can calculate the surface area of each triangular face of the pyramid:

Area = (√3 / 4) * s^2
Area ≈ (1.732 / 4) * 9.43^2
Area ≈ (1.732 / 4) * 89
Area ≈ 38.94 square feet

Since there are 4 triangular faces on the pyramid, the total amount of wrapping paper used is:

Total wrapping paper = 4 * Area
Total wrapping paper ≈ 4 * 38.94
Total wrapping paper ≈ 155.76 square feet

Therefore, Yusuf used approximately 155.76 square feet of wrapping paper.