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 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 + 90
Sum of areas of rectangles = 240 square units.
We also know,
Total surface area of the prism = Sum of areas of triangles + Sum areas of rectangles
Given, Total surface area of prism = 264 square units.
Therefore from the formula,
Sum of areas of triangles = Total surface area - sum of areas of reactangles
Sum of areas of triangles = 264 - 240
Sum of areas of triangles = 24 square units. (equation 3)
Let the missing dimension be 'h units'
From diagram,both triangles are congruent,hence have the same area
Area 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 get
6h = 24;
h = [tex]\frac{24}{6}[/tex]
Therefore,
h = 4 units.
Therefore,
The missing dimension is 4 units.
