Unifying Themes in Area Formulas

LENGTH × WIDTH

AREAS of Rectangles, Triangles, and Trapezoids Average width X height 𝑎+𝑏 2 ℎ h b

AREAS of Rectangles, Triangles, and Trapezoids b Average width X height 𝑏+𝑏 2 ℎ=𝑏ℎ h b

AREAS of Parallelograms, Triangles, and Trapezoids b Average width X height 𝑏+𝑏 2 ℎ=𝑏ℎ h b

AREAS of Rectangles, Triangles, and Trapezoids Average width X height 𝑏+0 2 ℎ= 𝑏ℎ 2 h b

Ellipses and Circles r 𝐴𝑟𝑒𝑎=𝜋 ∙𝑟 ∙𝑟=𝜋 𝑟 2 r

Ellipses and Circles b 𝐴𝑅𝐸𝐴= 𝜋 ∙𝑎 ∙𝑏=𝜋𝑎𝑏 a

Ellipses and Circles r Perimeter=2𝜋𝑟 r

Ellipses and Circles Perimeter ≈ 2𝜋 𝑎 2 + 𝑏 2 2 b a 2𝜋 𝑎 2 + 𝑏 2 2 b This works exactly when a=b=r on a circle a This is not exactly correct! You need Calculus to do this correctly!