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A Glass paperweight has the shape of a triangular prism. The bases are equilateral triangles with side lengths of 4 inches and a height of 3.5 inches. The height of the prism is 5 inches. find the lateral area and the total surface area of the paperwork.

Respuesta :

triangular prism has 2 equilateral triangular faces as bases and 3 lateral rectangle faces.
the dimensions are as follows 
equilateral triangle - sides - 4 inches each
                                 height - 3.5 inches
area of 1 equilateral triangle - 1/2 x side x height 
                                              = 1/2 x 4 inches x 3.5 inches
                                              = 7 sq.inches
As the base is an equilateral triangle, all 3 sides of the triangle are equal, hence, all the rectangles have the same breadth and height 
rectangle - length - 5 inches 
                  breadth - 4 inches 
area of 1 rectangle = length x breadth 
                                = 5 x 4 = 20 sq.inches

lateral area - area of the rectangle faces 
                   = 20 x 3 rectangle faces 
                  = 60 sq.inches
total surface area = base area + lateral area 
                              = (area of triangles x2) + 60
                              = (7x2) + 60 
total surface area = 74 sq.inches


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