Find the area of quadrilateral formed by joining points (4, 2), (8, 2), (4, 10) and (8, 14).

Let, the point A(4, 2), B(8, 2), C(8, 14) and D(4, 10).

Formula of triangle joining points (x1, y1), (x2, y2) and (x3, y3) →

Area, A = ½ {x1 × (x2 - x3) + x2 × (x3 - x2) + x3 × (x1 - x2)}

The area of triangle ABD from the given coordinates can be calculated from area of the triangle formulae,

In triangle ABD , (x1, y1) is (4, 2) , (x2, y2) is (8, 2) and (x3, y3) is (4, 10)

∴ A1= ½ {4 × (2 - 10) + 8 × (10 - 2) + 4 × (2 - 2)}

A1 = ½ ( - 32 + 64 + 0)

A1= 16 sq units.

Let A2 be the area of the triangle formed from BCD

Similarly, A2 = ½ {8 × (14 - 10) + 8 × (10 - 2) + 4(2 - 14)}

A2 = ½(32 + 64 - 48)

A2 = 24 sq units

The total area of the quadrilateral is A1 + A2 = 40 sq units.