Question

Find the area of the quadrilateral ABCd the coordinates of whose vertices are a(1,2 b(6,2) c(5,3) d(3,4) find Area quadrilateral

Answer 1

Let us divide the quadrilateral ABCD is divided into two triangles ABD and BCD.

Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD

Area of triangle with coordinates $(x_1,y_1), (x_2, y_2), (x_3,y_3)$ is given by the formula:

$\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)]$

Area of triangle ABD with coordinates A(1,2) B(6,2) and D(3,4)

Area of triangle ABD = $\frac{1}{2}[1(2-4)+6(4-2)+3(2-2)]$

Area of triangle ABD = $\frac{1}{2}[-2+12]$

= $\frac{10}{2} = 5$ square units.

Area of triangle BCD with coordinates B(6,2) C(5,3) D(3,4)

Area of triangle BCD = $\frac{1}{2}[6(3-4)+5(4-2)+3(2-3)]$

= $\frac{1}{2}[-6+10-3]$

= 0.5 square units.

Area of quadrilateral ABCD = Area of triangle ABD + Area of triangle BCD

= 5 + 0.5

= 5.5 square units.

Therefore, the area of the given quadrilateral ABCD is 5.5 square units.

Answer 2

Answer:

Step-by-step explanation: