Question

Which figure has the same area as the parallelogram shown below? A. A triangle with a base of 4 mm and a height of 20 mm B. A trapezoid with bases of 15 mm and 25 mm and a height of 2 mm C. A trapezoid with bases of 6 mm and 14 mm and a height of 8 mm D. A rectangle with base 30 mm and a height 8 mm

Answer 1

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 $80mm^{2}$, according to the following formula, which works for all rectangles and parallelograms:

$A_{parallelogram}=(b)(h)$   (1)

Where $b$ is the base and $h$ is the height

The area of a triangle is given by the following formula:

$A_{triangle}=\frac{1}{2}(b)(h)$   (2)

So, for option A:

$A_{triangle}=\frac{1}{2}(4mm)(20mm)=40mm^{2} \neq 80mm^{2}$    

Now, the area of a trapezoid is:

$A_{trapezoid}=\frac{1}{2}(b_{1}+ b_{2})(h)$   (3)

For option B:

$A_{trapezoid}=\frac{1}{2}(15mm+25mm)(2 mm)=40mm^{2} \neq 80mm^{2}$    

For option C:

$A_{trapezoid}=\frac{1}{2}(6mm+14mm)(8 mm)=80mm^{2}$>>>>This is the correct option!

For option D:

$A_{rectangle}=(30mm)(8mm)=240mm^{2} \neq 80mm^{2}$    

Therefore the correct option is C