two puzzles that involve side lengths and areas of rectangles

Question

Here are two puzzles that involve side lengths and areas of rectangles.

1. Find the missing area in Figure A.
2. Find the missing length in Figure B.

*Be sure to show or explain your reasoning and work!

Answer 1

a) the width of the blue box is 2 in (10 - 8). The length is 10 in (8 + 5 - 3). So the area is 20 sq in.

b) 60 sq in rectangle has length 12 in, so width must be 5 in . So length of 48 sq in rectangle must be 3 + 5 = 8 in and width must be 6 in. Width of 36 sq in rectangle must be 12 - 3 - (11-6) = 4 in. Therefore length of 36 sq in rectangle must be 9 in.