Question

Work in groups of three to answer the following question.

Higher Order Thinking Isabella has three rectangular cards
that are 4 inches by 5 inches. How can she arrange the cards,
without overlapping, to make one larger polygon with
the smallest possible perimeter? How will the area of the
polygon compare to the combined area of the three cards?

Answer 1

Explanation:

To arrange the three rectangular cards without overlapping to form a larger polygon with the smallest possible perimeter, Isabella can arrange the cards in a U-shape. That is, she can place two cards vertically next to each other and then place the third card horizontally on top of them to connect the two vertical cards. This will create a larger rectangle with dimensions of 8 inches by 5 inches.

The perimeter of this larger rectangle would be 2(8 + 5) = 26 inches, which is the smallest possible perimeter that can be obtained using these three rectangular cards.

The combined area of the three cards is:

3(4 x 5) = 60 square inches

The area of the larger rectangle formed by arranging the cards in a U-shape is:

8 x 5 = 40 square inches

Therefore, the area of the polygon formed by arranging the cards in this way is smaller than the combined area of the three cards.