Question

What is the area surface of the triangular prism? A. 448cm B.608cm C.704cm or D.640cm

Answer 1

608 cm^2

Explanation:

Find the area of the large rectangle

length is 10+12+10 = 32 and width is 16

A = 32*16 =512 cm^2

Then we have 2 triangle

The area of 1 is

A = 1/2 bh where b = 12 and h = 8

A = 1/2 ( 12 *8)

= 1/2 (96)

But we have 2 triangles

2 * 1/2 (96)

96 cm^2

Add the area of the large rectangle and the two triangles

512+96 =608 cm^2

Answer 2

608 squared centimeters.

Explanation:

To find the surface area of the net of the triangular prism, we can find the area of each individual shape and add them up.

For the net, we have 3 rectangles and 2 (congruent) triangles.

The left rectangle has a length of 16 and a width of 10. Thus, it's area is A=16(10)=160 squared centimeters.

The middle rectangle has a length of 16 and a width of 12. Thus, it's area is A=16(12)=192 squared centimeters.

The right rectangle has a length of 16 and a width of 10. Thus, it's area is identical to the left rectangle. It's area is 160 squared centimeters.

Now, for the two triangles, it's important to note they are the congruent since they belong to one triangular prism. Thus, we only need to figure out the area of one and then multiply by 2 to get the area of both of them.

One triangle has a base length of 12 and a height of 8. In other words, its area is (1/2)(12)(8)=48. Two of them will be 48(2) or 96.

Now, let's add all the areas together to find the surface area of the triangular prism. Thus, the area is:

96+160+160+192=608 squared centimeters.