A net of a triangular prism is shown below.
What is the surface area, in square centimeters, of the triangular prism?
Since the triangular prism is formed by two triangular bases and three rectangular faces, we can find the surface area by adding the area of all the faces.
The triangular bases have the same area.
Let's find the area of one of the triangular bases. The base of the triangle is 7 cm and the height of the triangle is 6 cm. The area of the triangle is $\frac{1}{2}bh=\frac{1}{2}(7\text{ cm})(6\text{ cm})=(3.5)(6)=21\text{ cm}^2$.
Since there are two triangular bases, their combined area is $2(21\text{ cm}^2)=42\text{ cm}^2$.
The three rectangular faces each have the same area. We need to find the area of one rectangular face. The length of the rectangle is 7 cm and the width of the rectangle is 6 cm. The area of the rectangle is $lw=7\text{ cm}\cdot 6\text{ cm}=42\text{ cm}^2$.
Since there are three rectangular faces, their combined area is $3(42\text{ cm}^2)=126\text{ cm}^2$.
The total surface area of the triangular prism is the combined area of the triangular bases and the rectangular faces. Therefore, the surface area is $42\text{ cm}^2 + 126\text{ cm}^2= \boxed{168}\text{ cm}^2$.