A triangular prism is a prism that has triangular bases. Let's take a look at the given diagram.
The surface area of a triangular prism is the sum of the areas of the two triangular bases and the three rectangular faces. Let's calculate the area of the triangular bases and the area of the rectangular faces one at a time. Then we can add them together.
Triangular Bases
The triangular bases of the given prism are isosceles triangles with 12 centimeter long side and 8 centimeter long height falling on that side. The area of a triangle is half the product of a base and the height falling onto that base. Let's use this fact to find the area of one of the prism's bases.
B = 1/2( 12)( 8) = 48
The area of one triangular base is 48 square centimeters. Because both of the triangular bases are exactly the same, we know that the area of the second triangular base is 48 square centimeters as well. Let's add them together!
Area of the Triangular Bases
48+48= 96cm^2
Rectangular Faces
Now, let's focus on the areas of the rectangular faces.
We can see that all three rectangular faces have a width of 3 centimeters. Also, their lengths are 10, 10, and 12 centimeters. Let's substitute the length and the width of each rectangle in the formula for the area of a rectangle to obtain their areas.
A=l w
Measures
Substitute
Evaluate
l= 10, w= 3
A= 10( 3)
A= 30cm^2
l= 10, w= 3
A= 10( 3)
A= 30cm^2
l= 12, w= 3
A= 12( 3)
A= 36cm^2
Surface Area of the Prism
Finally, to get the surface area of the triangular prism, we add the area of both triangular bases and the area of the three rectangular faces.
Surface Area of the Triangular Prism
96+ 30+ 30+ 36=192cm^2
