The surface area of the prism below is 264 square units . Find the missing dimensions of this prism. ( picture is in the picture).

Answer:The missing dimension is 4 units.Step-by-step explanation:In the given prism,Of all the surfaces,There are three rectangular surfaces and two triangular surfacesAnalyzing areas of rectangular surfaces:1)The two rectangles with dimensions of 15 units and 5 units: The area of each rectangle = Length of rectangle [tex]\times[/tex] Breadth of rectangle From the diagram, Length of rectangle = 15 units, Breadth of rectangle = 5 units. Area of each rectangle = 15[tex]\times[/tex] 5 ; Area of each rectangle = 75 square units. Sum of areas of the two rectangles = 2[tex]\times[/tex] 75 Sum of areas of the two rectangles = 150 square units (equation 1)2) The rectangle with the dimensions 15 units and 6 units: The area of thus rectangle=  Length of rectangle [tex]\times[/tex] Breadth of rectangle From the diagram, Length of rectangle = 15 units, Breadth of rectangle = 6 units. Area of the rectangle = 15[tex]\times[/tex] 6 ; Area of the rectangle = 90 square units. (equation 2)From equation 1 and equation 2,Therefore sum of areas of all rectangles in the prism = 150 + 90Sum of areas of rectangles = 240 square units.We also know,Total surface area of the prism = Sum of areas of triangles + Sum areas of rectanglesGiven, Total surface area of prism = 264 square units.Therefore from the formula,Sum of areas of triangles = Total surface area - sum of areas of reactanglesSum of areas of triangles = 264 - 240Sum of areas of triangles = 24 square units. (equation 3)Let the missing dimension be 'h units'Calculating sum of areas of triangles:From diagram,both triangles are congruent,hence have the same areaArea of a triangle = [tex]\frac{1}{2}\times base\times height[/tex]From diagram,Base = 6 units,Height = h units.Area of a triangle =[tex]\frac{1}{2}\times 6\times h[/tex] = 3h square units.Sum of the areas of both triangles = 3h+3h = 6h square units.Using equation 3, we get6h = 24;h = [tex]\frac{24}{6}[/tex]Therefore,h = 4 units.Therefore,The missing dimension is 4 units.