#### Question

If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) are the vertices of a quadrilateral, find the area of the quadrilateral ABCD

#### Solution

Joining B to D, we get two triangles ABD and BCD.

Area of ΔABD = `1/2 [-5(-5-5) - 4(5-7)+4(7+5)]`

`= 1/2 (50 + 8 + 48)`

`= 106/2`

= 53 sq units

Area of ΔBCD = `1/2 [-4(-6-5) - 1(5 + 5) + 4(-5 + 6)]`

`= 1/2 (44 - 10 + 4)`

`= 38/2`

= 19 sq units.

∴ Area of quad. ABCD = Area of ∆ABD + Area of ∆BCD = 53 + 19 = 72 sq units.

Is there an error in this question or solution?

Solution If A(–5, 7), B(–4, –5), C(–1, –6) and D(4, 5) Are the Vertices of a Quadrilateral, Find the Area of the Quadrilateral Abcd Concept: Area of a Triangle.