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Pennsylvania Keystone Geometry Formula Sheet

Aligned to the standard reference (draft — verify with your official source)

Pennsylvania’s Keystone Exams are the state’s end-of-course assessments — but it is worth knowing up front that the operational Keystone subjects are Algebra I, Biology, and Literature. Pennsylvania does not currently run a separate Geometry Keystone. This preset therefore serves the many Pennsylvania students who search for a “Keystone geometry formula sheet”: it is a curated high-school geometry set aligned to PA academic standards and to the geometry that appears within the Keystone Algebra I framework.

The set gathers the core high-school geometry formulas: area for triangles, rectangles, parallelograms, trapezoids, and circles; volume and surface area for rectangular prisms, cylinders, cones, spheres, and pyramids; the Pythagorean theorem; and the coordinate-geometry trio of distance, midpoint, and slope. The bonus section adds the rhombus, the special right triangles, SOH-CAH-TOA, and the equations of a line for students who want a fuller geometry review.

If you are preparing specifically for the Keystone Algebra I exam, the geometry you need is the subset that supports algebraic reasoning — coordinate geometry, slope, distance, and the Pythagorean theorem in particular. If you are reviewing a Pennsylvania high-school geometry course more broadly, the full set here maps to the standards your teacher is assessing throughout the year.

Because there is no official Geometry Keystone reference sheet to mirror, this preset is marked DRAFT and curated: use it as a study aid, and confirm with your teacher which formulas your specific assessment expects. Then pick A4 or US Letter, trim to your topics, and print a clean, verified two-column reference to study from.

For context, the Keystone Exams function as part of Pennsylvania’s graduation-pathway requirements, and the operational Algebra I exam does provide its own formula sheet that includes several geometry items — coordinate distance and slope among them. If your goal is that Algebra I Keystone, lean on the coordinate-geometry and right-triangle sections of this preset. If your teacher is preparing you for a district geometry final instead, the full set here gives you a complete, correct year-in-review to study from.

Official source: https://www.pa.gov/agencies/education.html — always confirm formulas against the current official document.

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Pennsylvania Keystone Geometry — Formula Sheet

Verified formulas · GeometryFormula.com

Rectangle
AreaA=l⋅wA = l \cdot w
PerimeterP=2(l+w)P = 2(l + w)
Diagonald=l2+w2d = \sqrt{l^2 + w^2}
Triangle
Area (base & height)A=12bhA = \tfrac{1}{2} b h
Area (Heron’s)A=s(s−a)(s−b)(s−c)A = \sqrt{s(s-a)(s-b)(s-c)}
Semiperimeters=a+b+c2s = \dfrac{a+b+c}{2}
PerimeterP=a+b+cP = a + b + c
Parallelogram
AreaA=bhA = b h
PerimeterP=2(a+b)P = 2(a + b)
Trapezoid
AreaA=12(a+b)hA = \tfrac{1}{2}(a + b)h
Medianm=a+b2m = \dfrac{a + b}{2}
Rhombus
AreaA=12d1d2A = \tfrac{1}{2} d_1 d_2
Sides=(d1/2)2+(d2/2)2s = \sqrt{(d_1/2)^2 + (d_2/2)^2}
PerimeterP=4sP = 4s
Circle
AreaA=πr2A = \pi r^2
CircumferenceC=2πrC = 2\pi r
Diameterd=2rd = 2r
Rectangular prism
VolumeV=lwhV = l w h
Surface areaSA=2(lw+lh+wh)SA = 2(lw + lh + wh)
Space diagonald=l2+w2+h2d = \sqrt{l^2 + w^2 + h^2}
Cylinder
VolumeV=πr2hV = \pi r^2 h
Lateral surfaceLSA=2πrhLSA = 2\pi r h
Surface areaSA=2πr(r+h)SA = 2\pi r(r + h)
Cone
Slant heightℓ=r2+h2\ell = \sqrt{r^2 + h^2}
VolumeV=13πr2hV = \tfrac{1}{3}\pi r^2 h
Lateral surfaceLSA=πrℓLSA = \pi r \ell
Surface areaSA=πr(r+ℓ)SA = \pi r(r + \ell)
Sphere
VolumeV=43πr3V = \tfrac{4}{3}\pi r^3
Surface areaSA=4πr2SA = 4\pi r^2
Pyramid
Slant heightℓ=(b/2)2+h2\ell = \sqrt{(b/2)^2 + h^2}
VolumeV=13b2hV = \tfrac{1}{3} b^2 h
Lateral surfaceLSA=2bℓLSA = 2 b \ell
Surface areaSA=b2+2bℓSA = b^2 + 2 b \ell
Distance formula
Distanced=(x2−x1)2+(y2−y1)2d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
Midpoint formula
MidpointM=(x1+x22,y1+y22)M = \left(\dfrac{x_1 + x_2}{2}, \dfrac{y_1 + y_2}{2}\right)
Slope
Slopem=y2−y1x2−x1m = \dfrac{y_2 - y_1}{x_2 - x_1}
Equations of a line
Slope-intercepty=mx+by = mx + b
Point-slopey−y1=m(x−x1)y - y_1 = m(x - x_1)
StandardAx+By=CAx + By = C
Pythagorean theorem
Right trianglea2+b2=c2a^2 + b^2 = c^2
Special right triangles
45–45–90x:x:x2x : x : x\sqrt{2}
30–60–90x:x3:2xx : x\sqrt{3} : 2x
Trig ratios (SOH-CAH-TOA)
Sinesin⁡θ=opphyp\sin\theta = \dfrac{\text{opp}}{\text{hyp}}
Cosinecos⁡θ=adjhyp\cos\theta = \dfrac{\text{adj}}{\text{hyp}}
Tangenttan⁡θ=oppadj\tan\theta = \dfrac{\text{opp}}{\text{adj}}
Free printable geometry formulas · GeometryFormula.com · CC BY-SA 4.0

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Frequently asked questions

What formulas are on the PA Keystone sheet?

Pennsylvania’s Keystone Exams are Algebra I, Biology and Literature — there is no operational Geometry Keystone. This is a curated high-school geometry set aligned to PA content. DRAFT — verify intent before use. Use the builder to see every formula, add bonus formulas, and print a clean A4 or US Letter copy.

Is this PA Keystone formula sheet free to print?

Yes — no sign-up, no watermark, no cost. Print it or save it as a PDF from your browser as often as you like.

Can I customize the sheet?

Yes. The preset pre-checks the aligned formulas; you can add or remove any formula, switch paper size, and copy a shareable link to your exact sheet.