Question

find the surface area

Explanation:

Step1: Calculate the base area

The base is a square with side length \(a = 10\) in. The area of a square is \(A_{base}=a^{2}\).

$$A_{base}=10^{2}=100\space in^{2}$$

Step2: Calculate the area of one triangular face

The base of each triangular face \(b = 10\) in and the slant height \(l=10\) in. The area of a triangle is \(A_{triangle}=\frac{1}{2}bl\).

$$A_{triangle}=\frac{1}{2}\times10\times10 = 50\space in^{2}$$

Step3: Calculate the total lateral surface area

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

$$A_{lateral}=4\times50=200\space in^{2}$$

Step4: Calculate the total surface area

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

$$A=100 + 200=300\space in^{2}$$

Answer:

\(300\space in^{2}\)