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Geometry Formula Sheet

A quick-reference sheet of essential geometry formulas. Covers area, perimeter, volume, surface area, circles, triangles, and coordinate geometry. Each formula links to its full definition page.

Triangle Formulas

Area of a Triangle
A=12bhA = \frac{1}{2}bh
Pythagorean Theorem
a2+b2=c2a^2 + b^2 = c^2
Heron's Formula
A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}
Triangle Angle Sum
A+B+C=180°A + B + C = 180°
Law of Sines
asin⁡A=bsin⁡B=csin⁡C\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}
Law of Cosines
c2=a2+b2−2abcos⁡Cc^2 = a^2 + b^2 - 2ab\cos C

Quadrilateral & Polygon Formulas

Area of a Rectangle
A=lwA = lw
Area of a Parallelogram
A=bhA = bh
Area of a Trapezoid
A=12(b1+b2)hA = \frac{1}{2}(b_1 + b_2)h
Polygon Angle Sum
S=(n−2)⋅180°S = (n-2) \cdot 180°
Each Angle (Regular)
θ=(n−2)⋅180°n\theta = \frac{(n-2) \cdot 180°}{n}

Circle Formulas

Circumference
C=2πr=πdC = 2\pi r = \pi d
Area of a Circle
A=πr2A = \pi r^2
Arc Length
s=rθ(θ in radians)s = r\theta \quad(\theta\text{ in radians})
Sector Area
A=12r2θA = \frac{1}{2}r^2\theta
Equation of a Circle
(x−h)2+(y−k)2=r2(x-h)^2 + (y-k)^2 = r^2

Volume Formulas

Rectangular Prism
V=lwhV = lwh
Cylinder
V=πr2hV = \pi r^2 h
Cone
V=13πr2hV = \frac{1}{3}\pi r^2 h
Sphere
V=43πr3V = \frac{4}{3}\pi r^3
Pyramid
V=13BhV = \frac{1}{3}Bh

Surface Area Formulas

Rectangular Prism
SA=2(lw+lh+wh)SA = 2(lw + lh + wh)
Cylinder
SA=2πr2+2πrhSA = 2\pi r^2 + 2\pi rh
Sphere
SA=4πr2SA = 4\pi r^2
Cone
SA=πr2+πrlSA = \pi r^2 + \pi r l

Coordinate Geometry

Distance
d=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}
Midpoint
M=(x1+x22,y1+y22)M = \left(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2}\right)
Slope
m=y2−y1x2−x1m = \frac{y_2-y_1}{x_2-x_1}

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