Find the area, in square units, of $$\triangle A B C$$ plotted below. ![](http://admin.getprephub.com/media/editor/ag14_20230214204459782034.png)

The coordinates of $$A, B, C, D$$ are given in the diagram. by distance formula. $$A B =\sqrt{(x_1-x_2)^{2}+(y_1-y_2)^{2}} $$ $$ =\sqrt{(-6-6)^{2}+(4-7)^{2}} $$ $$ =\sqrt{12^{2}+9} $$ $$ =\sqrt{144+9}=\sqrt{153} \text { unit } $$ $$CD =\sqrt{(4-2)^{2}+(6+2)^{2}} $$ $$ =\sqrt{4+64} $$ $$ =\sqrt{68} \text { unit }$$ Area of $$ \triangle A B C =\frac{1}{2} \times \text { base }(A B) \times \text { height }( CD) $$ $$=\frac{1}{2} \times \sqrt{153} \times \sqrt{68} \text { sq.unit } $$ $$=51 \text { sq. unit }$$

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Question

Difficulty Level:

Medium

MCQ

Find the area, in square units, of $\triangle A B C$ plotted below.

Select all that apply :

$51$

$48$

$96$

$102$

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