The given figure is a right triangular prism as we can see one of the sides having a right angle. The surface area is the sum of all the areas of all the faces of the prism.
Let us first find out the faces that the prism has
We can see that the prism has two right triangle bases at either sides
Then we can see that the sides are three rectangles.
So we are going to calculate the area of
two triangles with base = 9 cm, height = 12 cm
Three rectangles that has different lengths and widths
We need the third side of the triangle for this
Since its a right triangle and we have the two sides, we can use the pythagorean theorem to find the third side
[tex] c= \sqrt{{}a^{2}+ b^{2}} [/tex]
[tex] c =\sqrt{{}12^{2} +9^{2}} [/tex]
[tex] c =\sqrt{(144+81}} [/tex]
c= [tex] \sqrt{225} [/tex]
c=15
Now we have all the sides. Lets calculate the areas of each of the rectangles
R1 = Length × width = 15×18 = 270 sq.cm
R2 = 9×18 = 162 sq.cm
R3 = 12×18 = 216 sq.cm
The areas of the three rectangles are done
Now lets move on to the triangles
Area of triangle = [tex] \frac{1}{2} [/tex]× base ×height
= [tex] \frac{1}{2} [/tex] ×9×12 = 54 sq.cm
We have two triangular faces
That would make 54× 2 = 108 sq. cm
Lets add up all the areas
270+162+216+108( areas of two triangles) = 756 sq. cm
