Warm Up
Examine the two puzzles that involve side lengths and areas of rectangles. Can you find the missing area in Figure A and the missing length in Figure B? Be prepared to explain your reasoning.
Figure A
What is the missing area in Figure A above?
Enter the missing area.
Compare your answer:
To determine the area of the blue rectangle, we need to figure out it’s width and length.
The top shape is a square measuring 8 in. x 8 in. If the measurement of the longer left side is 10 inches, then the width of the blue rectangle can be an equation.
The width of the rectangle is 2 inches.
Because the bottom of the square is 8 inches, the length of the blue rectangle can be written as an equation. But we have an unknown .
If we look at the measurements of the smaller square, we see that we can use an equation to calculate .
Now, we can substitute the 2 for in the length equation.
The area of the blue rectangle is to equal 80 square inches.
Figure B
What is the missing length in Figure B above?
Enter the missing length.
Compare your answer:
You have to start with what you know and can figure out the other sides.
Sides of orange rectangle
Sides of green rectangle
Sides of combined rectangles
The measurement of the long side of combined orange and green rectangle will be equal. This helps figure out one side of the blue rectangle.
Sides of blue rectangle