Question

follow the steps to find the surface area of the square pyramid. what is the area of all 4 triangles? square base: 25 cm² triangles ×4: ? total sa: (diagram shows a square pyramid with base edges 5 cm and a 9 cm measurement, likely slant height)

Explanation:

Step1: Find base of triangle

The base of each triangular face is equal to the side length of the square base. Since the area of the square base is \(25\space cm^2\), the side length \(s\) of the square is \(\sqrt{25}=5\space cm\). So, the base of each triangle \(b = 5\space cm\).

Step2: Area of one triangle

The formula for the area of a triangle is \(A=\frac{1}{2}\times b\times h\), where \(b = 5\space cm\) (base) and \(h = 9\space cm\) (height of the triangle). Plugging in the values, we get \(A=\frac{1}{2}\times5\times9=\frac{45}{2} = 22.5\space cm^2\).

Step3: Area of 4 triangles

To find the area of all 4 triangles, we multiply the area of one triangle by 4. So, \(4\times22.5 = 90\space cm^2\).

Answer:

The area of all 4 triangles is \(\boldsymbol{90\space cm^2}\).