Geometry

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How do you go about finding the lateral area of a trianglar prism?

Ex: The base of a triangular prism is an equilateral triangle with a perimeter of 42 cm. If the height of the prism is 10 cm, find the lateral area.
Thanks for the help in advance

• Geometry -

Each of the three rectangular sides of the prism has an area of 14 x 10 = 140 cm^2. So there are 420 sq. cm of lateral area consisting of rectangles.

There are also two triangle sides. An equilateral triangle with 42 cm perimeter has 14 cm sides and a height of 14 sin 60 = 12.12 cm
The area of each triangular end is therefore
(1/2)x14x12.12 = 84.9 cm^2

Add 2 x 84.9 to 420 cm^2 for the answer.

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