Question

akira receives a prize at a science fair for having the most informative project. her trophy is in the shape of a square pyramid and is covered in shiny gold foil. image of a square pyramid with base edge 6 cm and slant height 15 cm how much gold foil did it take to cover the trophy, including the bottom? \boxed{} cm²

Explanation:

Step1: Calculate the area of the base

The base is a square with side length \(a = 6\) cm. The area of a square is \(A_{base}=a^{2}\).

$$A_{base}=6^{2}=36$$

Step2: Calculate the area of one triangular face

The formula for the area of a triangle is \(A_{\triangle}=\frac{1}{2}\times base\times height\). Here, the base of the triangle is \(b = 6\) cm and the height (slant height) \(h = 15\) cm.

$$A_{\triangle}=\frac{1}{2}\times6\times15 = 45$$

Step3: Calculate the total area of the four triangular faces

Since there are \(n = 4\) triangular faces, \(A_{triangles}=4\times A_{\triangle}\)

$$A_{triangles}=4\times45=180$$

Step4: Calculate the total surface area

The total surface area \(A = A_{base}+A_{triangles}\)

$$A=36 + 180=216$$

Answer:

\(216\)