Question

HELP!!!!!!! The square in the middle has an area of 1 square unit. What is the area of the entire rectangle in square units? Explain your reasoning.

Answer 1

Answer:

  4 square units

Step-by-step explanation:

If you draw a vertical line down the middle of the square, you divide it into two triangles that are congruent to the smaller triangles shown in the figure. Hence each of those triangles has an area of 1/2 square unit.

After you have divided the square as above, you see that two smaller triangles are identical in area to the larger triangles. So, each of those has an area of 2(1/2) = 1 square unit.

Then the total of areas is ...

  2 small triangles + square + 2 large triangles = 2(1/2) + 1 + 2(1) = 4

The area of the rectangle is 4 square units.