Question

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what is the surface area of this triangular prism? 15 cm 17 cm 40 cm 8 cm square centimeters

Explanation:

Step1: Calculate area of triangular faces

The triangular faces have base $b = 8$ cm and height $h=15$ cm. Area of a triangle $A_{triangle}=\frac{1}{2}bh$. So $A_{triangle}=\frac{1}{2}\times8\times15 = 60$ square - cm. Since there are 2 triangular faces, the total area of triangular faces $A_{1}=2\times60 = 120$ square - cm.

Step2: Calculate area of first rectangular face

One rectangular face has dimensions $l = 40$ cm and $w = 17$ cm. Area of a rectangle $A_{rect1}=40\times17=680$ square - cm.

Step3: Calculate area of second rectangular face

Another rectangular face has dimensions $l = 40$ cm and $w = 15$ cm. Area of a rectangle $A_{rect2}=40\times15 = 600$ square - cm.

Step4: Calculate area of third rectangular face

The third rectangular face has dimensions $l = 40$ cm and $w = 8$ cm. Area of a rectangle $A_{rect3}=40\times8=320$ square - cm.

Step5: Calculate total surface area

The total surface area $A$ of the triangular prism is the sum of the areas of all the faces. $A=A_{1}+A_{rect1}+A_{rect2}+A_{rect3}=120 + 680+600+320=1720$ square - cm.

Answer:

1720