Question

use the net for the triangular prism to find the surface area.

Explanation:

Step1: Calculate the area of the triangular bases

The formula for the area of a triangle is \(A=\frac{1}{2}bh\). Here, \(b = 6\) cm and \(h = 8\) cm.

$$ A_{triangle}=\frac{1}{2}\times6\times8= 24\space cm^{2} $$

Since there are two triangular bases, \(A_{total - triangles}=2\times24 = 48\space cm^{2}\)

Step2: Calculate the area of the rectangular faces

There are three rectangular faces.

• For the face with dimensions \(6\times10\): \(A_{1}=6\times10 = 60\space cm^{2}\)
• For the face with dimensions \(8\times10\): \(A_{2}=8\times10=80\space cm^{2}\)
• For the face with dimensions \(10\times10\) (hypotenuse of the triangle: using Pythagoras \(c=\sqrt{6^{2}+8^{2}}=\sqrt{36 + 64}=\sqrt{100} = 10\) cm, and length \(10\) cm): \(A_{3}=10\times10 = 100\space cm^{2}\)

The total area of the rectangular faces \(A_{total - rectangles}=60+80 + 100=240\space cm^{2}\)

Step3: Calculate the total surface area

The surface area \(A\) of the triangular prism is the sum of the area of the triangular bases and the rectangular faces.

$$ A=A_{total - triangles}+A_{total - rectangles} $$

$$ A = 48+240 $$

Answer:

\(288\space cm^{2}\)