Area Formulas
Triangle
Three formulae can be used to calculate the area of a triangle:
$$\newcommand{\ctext}[1]{\style{font-family:Arial}{\text{#1}}} \begin{align*} \ctext{Area}& =\frac12\times\ctext{base}\times\ctext{perpendicular height}=\frac12 bh \cr \ctext{Area}&=\frac12 ab\sin C \cr \ctext{Area}&=\sqrt{S(S-a)(S-b)(S-c)}\ctext{, where }S=\frac{a+b+c}{2} \end{align*}$$
Square
The area of a square can be found by multiplying its (equal) side lengths a.
$$\ctext{Area}=a^2$$
Rectangle
The area of a rectangle is found by multiplying its long and short side lengths (a and b respectively).
$$\ctext{Area}=ab$$
Trapezium
The area of a trapezium is found by multiplying it height h by the average of its two parallel side lengths (a and b)
$$\ctext{Area}=\frac{a+b}{2}\times h$$
Circle
The area of a circle is found by multiplying the constant $ \pi $ by the square of its radius r.
$$\ctext{Area}=\pi r^2$$
Sector of a Circle
The area of a sector of a circle is found by halving the product of the circle's radius, r, and the sector arc length, s.
$$\ctext{Area}=\frac12 rs$$
Segment of a Circle
The area of a segment of a circle is found by combining the circle's radius, r, segment arc length, s, chord length, c, and segment height, h.
$$\ctext{Area}=\frac12 rs-\frac12 c(r-h)=\frac12\left[rs-c(r-h)\right]$$
Ellipse
The area of an ellipse is calculated by multiplying the constant $ \pi $ by the product of the ellipse's semi-major axis (b) and semi-minor axis (a) lengths.
$$\ctext{Area}=\pi ab$$
Parabolic Segment
The area of a parabolic segment is found by combining the segment's base length, b, and height, h.
$$\ctext{Area}=\frac23 b\times h$$
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