Question

identify the solid that is represented by the net. then find its surface area. (all lengths are in yards.)

Explanation:

Step1: Identify the solid

The net represents a triangular prism. It has two triangular bases and three rectangular lateral - faces.

Step2: Find the area of the triangular bases

The base of the triangle can be found using the Pythagorean theorem. Let the base of the right - triangle be $b$. We know that the hypotenuse $c = 17$ and the height $h=15$. By $a^{2}+b^{2}=c^{2}$, we have $b=\sqrt{17^{2}-15^{2}}=\sqrt{(17 + 15)(17 - 15)}=\sqrt{32\times2}=\sqrt{64}=8$. The area of a triangle $A_{t}=\frac{1}{2}\times base\times height=\frac{1}{2}\times8\times15 = 60$ square yards. Since there are 2 triangular bases, the total area of the bases $A_{b}=2\times60 = 120$ square yards.

Step3: Find the area of the rectangular faces

There are three rectangular faces.
Face 1: Dimensions are $3\times17$, so its area $A_{1}=3\times17 = 51$ square yards.
Face 2: Dimensions are $3\times15$, so its area $A_{2}=3\times15 = 45$ square yards.
Face 3: Dimensions are $3\times8$, so its area $A_{3}=3\times8 = 24$ square yards.
The total area of the rectangular faces $A_{r}=51 + 45+24=120$ square yards.

Step4: Calculate the surface area

The surface area $A$ of the triangular prism is the sum of the area of the bases and the area of the rectangular faces. $A=A_{b}+A_{r}=120 + 120=240$ square yards.

Answer:

The solid is a triangular prism and its surface area is 240 square yards.