Question

Find the area of the quadrilateral ABCD whose vertices are A(3,-1), B(9,-5), C(14,0) and D(9,19).

Answer 1

for finding area of quadrilateral, the simplest way is dividing it and form two triangles and then find the area of two triangle and simply add it.

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hope it will help.

Answer 2

Answer:

Step-by-step explanation:

The vertices of the quadrilateral are:

A(3,-1), B(9,-5), C(14,0) and D(9,19).

Join A and C such that the quadrilateral gets divided into two triangles.

Now, using the formula for area of triangle using the coordinates, we have

Area of ΔABC,

$A=\frac{1}{2}(3(-5-0)+9(0+1)+14(-1+5))$

$A=\frac{|-15+9+56|}{2}=25 square units$

Area of ΔADC,

$A=\frac{1}{2}(3(19-0)+9(0+1)+14(-1-19))$

$A=\frac{|57+9-280|}{2}=107sq units$

Thus, the area of the quadrilateral is=area  ΔABC+areaΔADC

=25+107

=132 sq units.

Therefore, the area of quadrilateral is 132 sq units