To simplify such kinds of questions we draw a rectangle around the shape.
What is the length of any line on the graph?
The distance or length of any line on the graph,
[tex]d={\sqrt {(x_{{2}}-x_{{1}})^{{2}}+(y_{{2}}-y_{{1}})^{{2}}}},[/tex]
where,
d = distance/length of the line between point 1 and 2,
[tex](x_1, y_1)[/tex] = coordinate of point 1,
[tex](x_2, y_2)[/tex] = coordinate of point 2,
The correct option is A.
Explanation
Area of ΔRST = Area of the rectangle - (area of ΔA + area of ΔB + area of ΔC)
Area of ΔRST
[tex]Area\ of\ \triangle RST = (8\times 4) - [ (\frac{1}{2} \times 8\times 2) + (\frac{1}{2} \times 4\times 3) + (\frac{1}{2} \times 5\times 2) ][/tex]
Taking common term out (1/2),
[tex]Area\ of\ \triangle RST = (8\times 4) - [ (\frac{1}{2} \times 8\times 2) + (\frac{1}{2} \times 4\times 3) + (\frac{1}{2} \times 5\times 2) ]\\\\Area\ of\ \triangle RST = (8\times 4) - \frac{1}{2}[ ( 8\times 2) + ( 4\times 3) + ( 5\times 2) ]\\\\Area\ of\ \triangle RST = (8\cdot 4) - \frac{1}{2}[ ( 16) + ( 12) + ( 10) ][/tex]
Hence, the correct option is A.
Learn more about Area of Triangle:
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