Question

the net below is used to form a triangular prism. find the surface area of the prism it forms.

Explanation:

Step1: Calculate the area of the triangular faces

The formula for the area of a triangle is \( A=\frac{1}{2}bh \). Here, \( b = 4\ \text{yd} \) and \( h=2\ \text{yd} \).

$$ A_{\text{triangle}}=\frac{1}{2}\times4\times2 = 4\ \text{yd}^2 $$

Since there are \( 2 \) triangular faces, \( A_{triangles}=2\times4 = 8\ \text{yd}^2 \)

Step2: Calculate the area of the rectangular faces

There are \( 3 \) rectangular faces. Two of them have dimensions \( 8\times8 \) and one has dimensions \( 4\times8 \)

$$ A_{rect1}=8\times8 = 64\ \text{yd}^2 $$

$$ A_{rect2}=4\times8=32\ \text{yd}^2 $$

But wait, actually, using the formula for the surface area of a triangular prism \( SA = 2A_{\text{triangle}}+(a + b+ c)h\) (where \(a,b,c\) are the sides of the base triangle and \(h\) is the height of the prism). Here \(a = 8\), \(b = 8\), \(c = 4\), \(h = 8\) and \(A_{\text{triangle}}=4\)

$$ SA=2\times4+(8 + 8+4)\times8 $$

$$ SA = 8+(20)\times8 $$

$$ SA=8 + 72 $$

$$ SA=80\ \text{yd}^2 $$

Answer:

\( 80\ \text{yd}^2 \)