Geometry: Shapes and Formulas

Geometry Formulas

Geometry involves the study of shapes, sizes, positions, and properties of objects. To work with geometric figures, we use various formulas for calculating their perimeter, circumference, area, surface area, and volume.

The following diagram shows the Geometry Formulas for perimeter, circumference, area, surface area, and volume. Scroll down the page for more examples and solutions using the geometry formulas.

 

Geometry Worksheets
Practice your skills with the following worksheets:
Printable & Online Geometry Worksheets

A. 2D Geometry Formulas (Plane Shapes)
These shapes have only two dimensions (length and width) and are flat.
1. Square
Side length: s
Perimeter (P): P=4s
Area: A=s²
2. Rectangle
Length: l, Width: w
Perimeter (P): P=2l+2w or P=2(l+w)
Area: A=l×w
3. Triangle
Side lengths: a,b,c
Base: b, Height: h
Perimeter (P): P=a+b+c
Area: \(\frac{1}{2}bh\)
4. Circle
Radius: r, Diameter: d
Circumference: C=2πr or C=πd
Area: A=πr²
5. Parallelogram
Base: b, Height: h
Side lengths: a,b
Perimeter: P=2a+2b or P=2(a+b)
Area: A=bh
6. Trapezoid (or Trapezium)
Parallel bases: b₁,b₂
Height (distance between parallel bases): h
Other sides: c,d
Perimeter: P=b₁+b₂+c+d
Area: \(A=\frac{1}{2}\times \left( b_{1} + b_{2} \right)\times h\)

B. 3D Geometry Formulas (Solid Shapes)
These shapes have three dimensions (length, width, and height/depth) and occupy space. They have volume and surface area.
1. Cube
Side length: s
Volume: V=s³
Surface Area: SA=6s²
2. Rectangular Prism (Cuboid)
Length: l
Width: w
Height: h
Volume: V=l×w×h
Surface Area: SA=2(lw+lh+wh)
3. Cylinder
Radius of base: r
Height: h
Volume: V=πr²h
Curved Surface Area: CSA=2πrh
Total Surface Area: SA=2πrh+2πr²
4. Cone
Radius of base: r
Height: h
Slant Height: \(l=\sqrt{r^2+h^{2}}\)
Volume: \(V=\frac{1}{3}πr^2h\)
Curved Surface Area: CSA=πrl
Total Surface Area: SA=πrl+πr²
5. Sphere
Radius: r
Volume: \(V=\frac{4}{3}πr^3\)
Surface Area: SA=4πr²
6. Pyramid
Area of Base: B
Height: h
Volume: \(V=\frac{1}{3}Bh\)

Videos

The following videos will describe the common geometrical shapes and the corresponding formulas to calculate their area and perimeter. The videos also include the use of the Pythagorean Theorem and Heron’s formula.

Perimeter and area of triangles, rectangles, and trapezoids

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Area of triangles including Heron’s Formula. Pythagorean Theorem. Area and circumference of circle

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Surface Area of Circular Solids (cylinders, cones, spheres)

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Area and Circumference of circle. Solve word problems involving perimeter, area and right triangles

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A lesson on the basic formulas of geometry, including area and perimeter of rectangles, squares, circles and triangles

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