What is the surface area of the triangular prism A.810cm^2. b. 756cm^2 c. 972cm^2 d.1944cm^2

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 hasWe can see that the prism has two right triangle bases at either sidesThen 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 cmThree rectangles that has different lengths and widthsWe need the third side of the triangle for thisSince 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=15Now we have all the sides. Lets calculate the areas of each of the rectanglesR1 = Length × width = 15×18 = 270 sq.cmR2 = 9×18 = 162 sq.cmR3 = 12×18 = 216 sq.cmThe areas of the three rectangles are doneNow lets move on to the trianglesArea of triangle = [tex] \frac{1}{2} [/tex]× base ×height = [tex] \frac{1}{2} [/tex] ×9×12 = 54 sq.cmWe have two triangular facesThat would make 54× 2 = 108 sq. cmLets add up all the areas270+162+216+108( areas of two triangles) = 756 sq. cm