Question

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what is the surface area of this triangular prism? 12 mm 60 mm 15 mm 9 mm square millimeters

Explanation:

Step1: Calculate area of triangular faces

The area of a triangle is $A=\frac{1}{2}bh$. Here, $b = 9$ mm and $h=12$ mm. So, $A_{triangle}=\frac{1}{2}\times9\times12= 54$ $mm^{2}$. Since there are 2 triangular faces, the total area of triangular faces is $2\times54 = 108$ $mm^{2}$.

Step2: Calculate area of first rectangular face

The dimensions of the first rectangular face are length $l = 60$ mm and width $w=9$ mm. So, $A_{rect1}=60\times9 = 540$ $mm^{2}$.

Step3: Calculate area of second rectangular face

The dimensions of the second rectangular face are length $l = 60$ mm and width $w = 12$ mm. So, $A_{rect2}=60\times12=720$ $mm^{2}$.

Step4: Calculate area of third rectangular face

The dimensions of the third rectangular face are length $l = 60$ mm and width $w = 15$ mm. So, $A_{rect3}=60\times15 = 900$ $mm^{2}$.

Step5: Calculate total surface - area

The total surface area $A$ of the triangular prism is the sum of the areas of the triangular and rectangular faces. $A=108 + 540+720 + 900=2268$ $mm^{2}$.

Answer:

2268