The semiperimeter on a figure is defined as s congruent 1/2 p, where p is the perimeter. The semiperimeter of polygons appears in unexpected ways in the computation of their areas. The most notable cases are in the altitude, exradius, and inradius of a triangle, the Soddy circles, Heron's formula for the area of a triangle in terms of the legs a, b, and c A_Δ = sqrt(s(s - a)(s - b)(s - c)), and Brahmagupta's formula for the area of a quadrilateral A_quadrilateral = sqrt((s - a)(s - b)(s - c)(s - d) - a b c d cos^2((A + B)/2)).
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