Measuring Space Perimeter and Area

Perimeter of square: 4a [a = side length]

Perimeter of equilateral triangle: 3a [a = side length]

Perimeter of rectangle: 2(a+b) [a = length, b = width]

Circumference of circle: C = πd = 2πr [d = diameter, r = radius]

Length of arc: l = 2\pi r × \frac{\theta^\circ}{360^\circ} [r = radius, θ = central angle in degrees]

The area of a rectangle with sides a and b units is ab sq units, with unit area defined as a 1×1 square.

The area of a parallelogram equals base × height.

Area of triangle (base-height): A = 1/2 bh [b = base, h = height]

Heron's formula: \sqrt{s(s-a)(s-b)(s-c)}, s=\frac{1}{2}(a+b+c) [a,b,c = sides of triangle, s = semi-perimeter]

Area of triangle via circumradius: \frac{abc}{4R} [a,b,c = sides, R = circumradius]

Area of triangle via inradius: \frac{r(a+b+c)}{2} [a,b,c = sides, r = inradius]

Brahmagupta's formula (cyclic 4-gon): \sqrt{(s-a)(s-b)(s-c)(s-d)}, s=\frac{1}{2}(a+b+c+d) [a,b,c,d = sides of cyclic quadrilateral, s = semi-perimeter

For a rectangle, Brahmagupta's formula correctly reduces to area = ab.

Baudhāyana's construction for squaring a rectangle uses the identity ((a+b)/2)² - ((a-b)/2)² = ab.