Math logo

Math


Area of a quadrilateral

A quadrilateral is a geometric shape that has 4 sides and 4 vertices. Here I am talking about a quadrilateral that has no equal sides or equal angles. The area of such a quadrilateral can be calculated in many ways but I chose one of them.

Area of a quadrilateral

1 ÷ 4 √ 4 × p2 × q2 - (a2 + c2 - b2 - d2)2

Where:
p and q are the diagonals of the quadrilateral.
a, b, c, and d are the sides of the quadrilateral.

Example:
If p = 26, q = 22, a = 20, b = 18, c = 8, and d = 24
then A = ?

1 ÷ 4 √ 4 × p2 × q2 - (a2 + c2 - b2 - d2)2 =
1 ÷ 4 √ 4 × 262 × 222 - (202 + 82 - 182 - 242)2 =
1 ÷ 4 √ 4 × 676 × 484 - (400 + 64 - 324 - 576)2 =
1 ÷ 4 √ 1308736 - (- 436)2 =
1 ÷ 4 √ 1308736 - 190096 =
1 ÷ 4 √ 1118640 =
1057 ÷ 4 = 265