Question

what is the surface area of the shape?

Explanation:

Step1: Find area of each face

The shape is a triangular pyramid. There are \(4\) triangular faces.
For the two triangles with base \(2\) in and height \(2\) in: Area \(A_1=\frac{1}{2}\times2\times2 = 2\) in² each.
For the triangle with base \(2\) in and height \(3\) in: Area \(A_2=\frac{1}{2}\times2\times3=3\) in².
For the largest triangle (by combining the bases and heights from the structure, assume it's calculated as \(\frac{1}{2}\times(2 + 2)\times3\)): Area \(A_3=\frac{1}{2}\times4\times3 = 6\) in².

Step2: Sum up all areas

Total surface area \(S=2\times A_1+A_2 + A_3\).
Substitute values: \(S = 2\times2+3 + 6\).
\(S=4 + 3+6=13\) in².

Answer:

\(13\)