Question

which diagram is a net for this prism? what is the surface area of the triangular prism? square feet

Explanation:

Step1: Identify the prism's components

The triangular - prism has two triangular bases and three rectangular faces. The triangular bases have sides 10 ft, 10 ft, and 12 ft, and the height of the triangular base (from the 12 - ft side to the opposite vertex) can be found using the Pythagorean theorem. The height $h$ of the triangle: $h=\sqrt{10^{2}-6^{2}}=\sqrt{100 - 36}=\sqrt{64}=8$ ft. The rectangular faces have dimensions: two with dimensions 10 ft by 13 ft and one with dimensions 12 ft by 13 ft.

Step2: Calculate the area of the triangular bases

The area formula for a triangle is $A_{triangle}=\frac{1}{2}\times base\times height$. For the triangular base with base = 12 ft and height = 8 ft, $A_{triangle}=\frac{1}{2}\times12\times8 = 48$ square feet. Since there are 2 triangular bases, the total area of the bases is $2\times48=96$ square feet.

Step3: Calculate the area of the rectangular faces

The area of the two 10 - ft by 13 - ft rectangular faces is $2\times(10\times13)=260$ square feet. The area of the 12 - ft by 13 - ft rectangular face is $12\times13 = 156$ square feet.

Step4: Calculate the total surface area

The total surface area $A$ of the triangular prism is the sum of the areas of the bases and the rectangular faces. $A=96 + 260+156=512$ square feet.

Answer:

512