Question

Find the surface area of each prism

Answer 1

3. SA = 876
`in^(2)`

4. SA = 161
`ft^(2)`

Explanation:

Number 3.

To find the total Surface Area, we need to know all the side lengths which are used to multiply to find the Area of each side. Then add the areas of all the sides to get the total SA.

To find side lengths:

Assuming the back triangle (24, 10 in) is congruent to the front triangle (26in.): First, Knowing the Pythagorean triples or the Pythagorean theorem, we can conclude that the short bottom leg in the triangle on the right (6, 10, x in) is 8 in. Secondly, to find the leg of the triangle with a hypotenuse of 24 inches, we subtract: 26 - 8 = 18 in.

Now we know all the (needed) side lengths.

To find the Surface Area:

Total SA = (12 x 26) + (12 x 24) + (12 x 10) + 2 x ((6 x 18 x 0.5) + (6 x 8 x 0.5))

= 312 + 288 + 120 + 2 x (54 + 24) = 720 + (2 x 78)

= 876
`in^(2)`

Number 4.

Same Idea: To find the Total SA, we need to know all the side lengths which are used to multiply to find the Area of each side. Then add the areas of all the sides to get the total SA.

Assuming the back triangle (7ft) is congruent to the front triangle (5x5 ft), then in this case, we already know all the needed side lengths.

To find the Surface Area:

Total SA = 2 x (8 x 5) + 2 x (5 x 5 x 0.5) + (7 x 8)

= 80 + 25 + 56

= 161
`ft^(2)`