Question

area of triangles and parallelograms
how do the areas of the parallelograms compare?
the area of parallelogram abcd is 4 square units greater than the area of parallelogram efgh
the area of parallelogram abcd is equal to the area of parallelogram efgh
the area of parallelogram abcd is 2 square units greater than the area of parallelogram efgh

Explanation:

Step1: Recall area formula for parallelogram

The area formula for a parallelogram is $A = base\times height$.

Step2: Determine base and height of parallelogram EFGH

Counting the grid - squares, for parallelogram EFGH, if we consider the base along the horizontal direction, the base length $b_{EFGH}= 4$ units and the height $h_{EFGH}=3$ units. So, $A_{EFGH}=b_{EFGH}\times h_{EFGH}=4\times3 = 12$ square units.

Step3: Determine base and height of parallelogram ABCD

For parallelogram ABCD, if we consider the base along the horizontal direction, the base length $b_{ABCD}=4$ units and the height $h_{ABCD}=4$ units. So, $A_{ABCD}=b_{ABCD}\times h_{ABCD}=4\times4 = 16$ square units.

Step4: Compare the areas

$A_{ABCD}-A_{EFGH}=16 - 12=4$ square units. So the area of parallelogram ABCD is 4 square units greater than the area of parallelogram EFGH.

Answer:

The area of parallelogram ABCD is 4 square units greater than the area of parallelogram EFGH.