Question

The points A, B, C, D have respective co-ordinates (-2, -3), (6, -5) , (18, 9) and (0, 12). Find the area of quadrilateral ABCD.

• A. 200
• B. 195
• C. 206
• D. 350

Answer 1

The correct option is C 206

Area of the quadrilateral ABCD
= area of the triangle ABC + area of the triangle ACD

Area of a triangle
$=\frac{1}{2}$ [$x_1$( $y_2$ - $y_3$) + $x_2$( $y_3$ - $y_1$) + $x_3$( $y_1$ - $y_2$)]

So, the area of the triangle ABC

$=\frac{1}{2}|(10+54-54)-(-18-90-18)|$

$=\frac{1}{2}(10+126)$

$=\frac{1}{2}\left(136\right)$

= 68 sq. units.

And, area of the triangle ACD

$=\frac{1}{2}|(-18+216+0)-(-54+0-24)|$

$=\frac{1}{2}(198+78)$

$=\frac{1}{2}\left(276\right)$

= 138 sq. units.

Therefore, the required area of the quadrilateral ABCD

= area of the ∆ ABC + area of the ∆ACD

= (68 + 138) sq. units

= 206 sq. units.