Explanation
We are to find the total area of the triangular prism
To do so, we will have to split the triangle into 5 parts labeled A, B, C. D, and E as shown below
The total area of the prism is the area of the individual parts
For part A, we will have to get the other dimension of the base
We will get x using the Pythagoras theroem
[tex]x^=\sqrt{10^2-6^2}=\sqrt{100-36}=\sqrt{64}=8[/tex]
The value of x is 8
So we can now proceed to get the areas as follow
Part A
[tex]Area\text{ of triangle}=\frac{1}{2}\times8\times6=24cm^2[/tex]
Part B and part A are similar, they have the same area
So area of part B = part A = 24 cm²
For part E
Area is
[tex]Area\text{ of rectangle =length}\times breadth=22\times8=176cm^2[/tex]
For part D
Area of rectangle is length x breadth =
[tex]10cm\times22cm=220cm^2[/tex]
Part C
Area is given as length x breadth
[tex]6cm\times22cm=132cm^2[/tex]
So, we will sum all the areas to find the total area to be
[tex]24+24+176+220+132=576cm^2[/tex]
Thus, the area of the triangular prism is 576cm²
