Surface Area with Nets - Pre Algebra

1. What is the surface area formula for a rectangular prism with length $l$, width $w$ and height $h$?

   $SA = 2(lw + lh + wh)$, one term for each pair of opposite faces.

2. What is the surface area of a rectangular prism that is 3 ft by 5 ft by 8 ft?

   158 square feet, since $2(15 + 24 + 40) = 2(79)$.

3. A square pyramid has base edge 6 cm and slant height 5 cm. What is its surface area?

   96 square centimeters. Base $36$ plus four triangles of $\frac{1}{2}(6)(5) = 15$ each.

4. What is the surface area of a rectangular prism that is 6 cm by 4 cm by 9 cm?

   228 square centimeters, since $2(24 + 54 + 36) = 2(114)$.

5. What faces make up the net of a rectangular prism?

   Six rectangles in three pairs of congruent opposite faces.

6. How does the surface area of a prism change when it is unfolded into a different net?

   It stays the same. Every net of the prism is made of the same faces, just arranged differently.

7. What kind of units does surface area use?

   Square units, such as square centimeters, because it measures the area of the faces.

8. What faces make up the net of a square pyramid?

   One square base and four triangles.

9. What is a net of a three-dimensional figure?

   A flat pattern of its faces that folds into the figure. The area of the net equals the figure's surface area.

10. What is the surface area of a cube with edge length 5 in?

    150 square inches. Six square faces, each $5 \times 5 = 25$.

11. What faces make up the net of a triangular prism?

    Two triangles (the bases) and three rectangles (the lateral faces).

12. A triangular prism has right triangle bases with sides 3, 4 and 5 cm, and length 10 cm. What is its surface area?

    132 square centimeters. Two bases of 6 each, plus rectangles $(3 + 4 + 5)(10) = 120$.

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