Question

this is a parallelogram.7 m5 m6 mwhich shows the parallelogram cut and rearranged into a rectangle?7 m5 m7 m5 m6 m6 mwhat is the area of the parallelogram?$square$ square meters

Explanation:

Step1: Identify valid rearrangement

The parallelogram has base $6\ \text{m}$, height $5\ \text{m}$, and side $7\ \text{m}$. To rearrange to a rectangle, the rectangle must have length $6\ \text{m}$ and height $5\ \text{m}$, with the $7\ \text{m}$ side as the diagonal. The first option matches this (right angle at $6\ \text{m}$ base, $7\ \text{m}$ side, $5\ \text{m}$ height, diagonal $5\ \text{m}$ is incorrect; the first option has right angle at $6\ \text{m}$ and $7\ \text{m}$ corner, diagonal $5\ \text{m}$ is wrong, correction: the correct rectangle has base = parallelogram base ($6\ \text{m}$) and height = parallelogram height ($5\ \text{m}$), so the first rectangle (left one) with $6\ \text{m}$ base, $7\ \text{m}$ side, right angle at $6\ \text{m}$ and $7\ \text{m}$ is wrong, correction: the correct rearrangement uses the height $5\ \text{m}$ as the side of the rectangle, so the left rectangle has $6\ \text{m}$ base, $7\ \text{m}$ side, diagonal $5\ \text{m}$ is wrong, the right rectangle has $6\ \text{m}$ base, $5\ \text{m}$ side, diagonal $7\ \text{m}$ which is correct, as the parallelogram's side is $7\ \text{m}$, which becomes the diagonal of the rectangle.

Step2: Calculate parallelogram area

Use area formula: $\text{Area} = \text{base} \times \text{height}$
$\text{Area} = 6 \times 5 = 30$

Step1: Select valid rectangle

Parallelogram base $6\ \text{m}$, height $5\ \text{m}$, side $7\ \text{m}$. Rearranged rectangle has sides $6\ \text{m}$ and $5\ \text{m}$, diagonal $7\ \text{m}$. This matches the right option.

Step2: Compute area

Use $\text{Area} = b \times h$
$\text{Area} = 6 \times 5 = 30$

Answer:

1. The correct rearrangement is the left option: <the rectangle with 7 m side, 6 m base, right angle at the 6 m and 7 m corner, and 5 m diagonal>
2. $30$ square meters

Correction for the rearrangement:
The correct rectangle is the left one? No, wait, the parallelogram has base 6, height 5, side 7. When you cut the right triangle from the parallelogram (with height 5, base equal to the extra length), you move it to the left to make a rectangle of length 6, height 5, so the rectangle has sides 6 and 5, diagonal 7. So the right option is the correct rearrangement: the rectangle with 6 m base, 5 m side, right angle at 6 m and 5 m, diagonal 7 m.

Final Answer:

1. The correct rearrangement is the right option: <rectangle with 6 m base, 5 m vertical side, right angle at the bottom right, and 7 m diagonal>
2. $30$ square meters

Proper step-by-step: