Perimeters And Areas Of Plane Figures — Formula Sheet

Rectangle: Perimeter = 2(l+b); Area = lb

Square: Perimeter = 4a; Area = a^2; Diagonal = a√2

Triangle (base-height): Perimeter = a+b+c; Area = 1/2 × b × h

Heron's Formula: Area = √(s(s-a)(s-b)(s-c)), s = (a+b+c)/2

Parallelogram: Area = b × h

Area of path around a rectangle of dimensions l×b with width w = (l+2w)(b+2w) − lb

Area of two cross paths through middle of rectangle = w(l+b) − w^2

For two cross paths, simplified form = w(l+b−w)

A square uses perimeter 4a, area a^2, and diagonal a√2.

Example with sides 5 cm, 6 cm, and 7 cm gives area 6√6 cm².

For a path of width w around a rectangle of dimensions l × b, area = (l+2w)(b+2w) − lb.

Aryabhata (476–550 AD) gave π ≈ 62832/20000 = 3.1416.

Square area = a^2 and diagonal = a√2.

Triangle area using base and height = 1/2 × b × h.

Cross paths formula = w(l+b) - w².

For a circle of radius r, circumference = 2πr and area = πr^2.

The chapter uses π ≈ 22/7 and also notes Aryabhata’s value π ≈ 3.1416.