Question

solve & discuss it!
sofia drew the grid below and plotted the points a, b, c, and d. connect point a to b, b to c, c to d, and d to a. then find the area of the shape and explain how you found it. using the same grid, move points b and c four units to the right. connect the points to make a new parallelogram abcd. what is the area of this shape?

Explanation:

Since the grid with points A, B, C, D is not shown, we'll assume a typical parallelogram scenario (since moving B and C right makes a parallelogram, so original is also a parallelogram). For a parallelogram, area = base × height.

Step 1: Original Parallelogram (Assumption)

Suppose the base (length of AB or DC) is \( b \) and height (vertical distance between the bases) is \( h \). For example, if original base is, say, 4 units and height is 3 units, area would be \( 4 \times 3 = 12 \) (but this depends on grid).

Step 2: After Moving B and C

Moving B and C 4 units right: in a parallelogram, moving two adjacent vertices (B and C) horizontally (right) doesn’t change the base length or the height (since height is vertical distance). So base \( b \) and height \( h \) remain same. Thus, area remains \( b \times h \), same as original.

(Note: Without the grid, we use the property of parallelograms: area is base × height, and horizontal translation of B/C doesn’t affect base or height. If original grid had, e.g., base = 5, height = 2, area = 10, and after moving, area is still 10.)

Answer:

The area of the new parallelogram is equal to the area of the original parallelogram (depends on grid, but using the property of parallelogram area = base × height, and translation doesn’t change base/height, so area remains the same as original). For example, if original area was 12, new area is 12.