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The triangular faces of the prism shown are equilateral triangles with perimeter 30 cm. Use a net to find the surface area of the prism.
[tex]\begin{gathered} The\text{ surface area is made up of the two equilateral triangles shown above as well as the three rectangles.} \\ Area\text{ of Triangles = 2\lparen}\frac{1}{2}b*h) \\ If\text{ the perimeter of the triangle is 30cm, the length of one side = 30/3 = 10 = base} \\ Area\text{ = 2\lparen}\frac{1}{2}*10*8.7) \\ \text{ =87} \\ Area\text{ of the three rectangles = 3\lparen length*width\rparen } \\ \text{ =3\lparen10*12\rparen} \\ \text{ =360} \\ Total\text{ Surface Area = 360 + 87 = 447} \end{gathered}[/tex]
Surface Area of the two triangles in the net = 2*(0.5*b*h)
= 2*(0.5*10*8.7)
=87
Surface Area of three rectangles in the net = 3(l*b)
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