Geometry / Unit 11: Area, Surface Area and Volume
11.1 Area of Polygons
Notes
Area is the space inside a flat figure, measured in square units. The height is always perpendicular to the base.
- Rectangle or parallelogram: $A = bh$. Triangle: $\displaystyle A = \frac{1}{2}bh$.
- Trapezoid: $\displaystyle A = \frac{1}{2}(b_1 + b_2)h$.
- Rhombus or kite: $\displaystyle A = \frac{1}{2}d_1 d_2$ (diagonals).
- Regular polygon: $\displaystyle A = \frac{1}{2}aP$, where $a$ is the apothem (center to midpoint of a side) and $P$ is the perimeter.
- Example: a trapezoid with bases 6 and 10 and height 4 has $\displaystyle A = \frac{1}{2}(16)(4) = 32$.
Practice
Find the area of a trapezoid with bases 8 and 14 and height 5.
$\displaystyle \frac{1}{2}(8 + 14)(5) = 55$.
A triangle has a base of 12 and a height of 7. Find its area.
$\displaystyle \frac{1}{2}(12)(7) = 42$.
A regular hexagon has a side of 6 and an apothem of $\displaystyle 3\sqrt{3}$. Find its area.
$P = 36$, so $\displaystyle A = \frac{1}{2}(3\sqrt{3})(36) = 54\sqrt{3}$.
Ready for more? Take the Unit 11 test.