Exercise 1 Page 777

A triangular prism is a prism that has triangular bases. Let's take a look at the given diagram.

We can use the net of this prism to find its surface area. 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

Looking at the net of this solid, for now let's think only about the triangular bases. We can see that one of the triangular bases has a base of $51$ yards and a height of $12$ yards. Let's find its area by substituting these values into the formula for the area of a triangle. The area of one triangular base is $306$ square yards. Because both of the triangular bases are exactly the same, we know that the area of the second triangular base is $306$ square yards as well. Let's add them together!

Rectangular Faces

Now let's look at the rectangular faces. We can see that all three rectangular faces have a width of $5$ yards. Also, their lengths are $37,$ $51,$ and $20$ yards. Let's substitute the length and the width of each rectangle in the formula for the area of a rectangle to obtain their areas.

$A=\ell w$
Measures	Substitute	Evaluate
$\ell =37,$ $w=5$	$A=37(5)$	$A=185{\text{ yd}}^2$
$\ell =51,$ $w=5$	$A=51(5)$	$A=255{\text{ yd}}^2$
$\ell =20,$ $w=5$	$A=20(5)$	$A=100{\text{ yd}}^2$

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.