Answer: A trapezoid with bases of 6 mm and 14 mm and a height of 8 mm
The parallelogram in the figure has an area of [tex]80mm^{2}[/tex], according to the following formula, which works for all rectangles and parallelograms:
[tex]A_{parallelogram}=(b)(h)[/tex] (1)
Where [tex]b[/tex] is the base and [tex]h[/tex] is the height
The area of a triangle is given by the following formula:
[tex]A_{triangle}=\frac{1}{2}(b)(h)[/tex] (2)
So, for option A:
[tex]A_{triangle}=\frac{1}{2}(4mm)(20mm)=40mm^{2} \neq 80mm^{2}[/tex]
Now, the area of a trapezoid is:
[tex]A_{trapezoid}=\frac{1}{2}(b_{1}+ b_{2})(h)[/tex] (3)
For option B:
[tex]A_{trapezoid}=\frac{1}{2}(15mm+25mm)(2 mm)=40mm^{2} \neq 80mm^{2}[/tex]
For option C:
[tex]A_{trapezoid}=\frac{1}{2}(6mm+14mm)(8 mm)=80mm^{2} [/tex]>>>>This is the correct option!
For option D:
[tex]A_{rectangle}=(30mm)(8mm)=240mm^{2} \neq 80mm^{2} [/tex]
Therefore the correct option is C
