Question

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

Answer 1

D is the answer 12 x 9 =108. 108 x 18 =1944

Answer 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 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

$c= \sqrt{{}a^{2}+ b^{2}}$

$c =\sqrt{{}12^{2} +9^{2}}$

$c =\sqrt{(144+81}}$

c= $\sqrt{225}$

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 = $\frac{1}{2}$× base ×height

= $\frac{1}{2}$ ×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