Homework on solids, cubes, prisms, and shapes, including formulas for area and volume.

Here are the formulas for the given solids and shapes:

Solids

• Cube Let $s$ be the side length.

  • Area (Surface Area): $\boxed{6s^2}$
  • Volume: $\boxed{s^3}$

• Triangular Prism Let $b$ be the base length of the triangular face, $h_t$ be the height of the triangular face, $s_1, s_2, s_3$ be the side lengths of the triangular face, and $L$ be the length (height) of the prism.

  • Area (Surface Area): $\boxed{b h_t + (s_1 + s_2 + s_3)L}$
  • Volume: $\boxed{\frac{1}{2} b h_t L}$

• Rectangular Prism Let $l$ be the length, $w$ be the width, and $h$ be the height.

  • Area (Surface Area): $\boxed{2(lw + lh + wh)}$
  • Volume: $\boxed{lwh}$

Shapes

• Rectangle Let $l$ be the length and $w$ be the width.

  • Perimeter: $\boxed{2(l+w)}$
  • Area: $\boxed{lw}$

• Square Let $s$ be the side length.

  • Perimeter: $\boxed{4s}$
  • Area: $\boxed{s^2}$

• Circle Let $r$ be the radius.

  • Perimeter (Circumference): $\boxed{2\pi r}$
  • Area: $\boxed{\pi r^2}$

• Triangle Let $b$ be the base length, $h$ be the height, and $a, c$ be the other two side lengths of the triangle.

  • Perimeter: $\boxed{a+b+c}$
  • Area: $\boxed{\frac{1}{2} b h}$