Question

a triangular prism is shown below. which diagram is a net for this prism? what is the surface area of the triangular prism?

Explanation:

Step1: Identify the faces of the prism

A triangular prism has 2 triangular faces and 3 rectangular faces. The two triangular faces have base - 10 mm and height - 24 mm. The three rectangular faces have dimensions: 20×10, 20×26, 20×24.

Step2: Calculate the area of the triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. For $b = 10$ mm and $h=24$ mm, $A_{triangle}=\frac{1}{2}\times10\times24=120$ $mm^{2}$. Since there are 2 triangular faces, the total area of the triangular faces is $2\times120 = 240$ $mm^{2}$.

Step3: Calculate the area of the rectangular faces

For the first rectangular face with dimensions 20×10, $A_1=20\times10 = 200$ $mm^{2}$. For the second rectangular face with dimensions 20×26, $A_2=20\times26=520$ $mm^{2}$. For the third rectangular face with dimensions 20×24, $A_3=20\times24 = 480$ $mm^{2}$. The total area of the rectangular faces is $A_{rectangles}=200 + 520+480=1200$ $mm^{2}$.

Step4: Calculate the surface area

The surface area $A_{total}$ of the triangular prism is the sum of the area of the triangular faces and the area of the rectangular faces. So $A_{total}=240 + 1200=1440$ $mm^{2}$.

Answer:

$1440$ $mm^{2}$