Aimathic
Login | English | Deutsch

Free Math Worksheets

Build your own math worksheets from 21,000 problems for grades 3 to 12, from fractions to calculus. Every problem includes step-by-step solutions.

Relate area to multiplication

Click problems to add them to your worksheet.

5317153
Two figures, Figure A and Figure B, are shown on a geoboard. The small gray square in the lower-right corner represents one unit square. a) Find the area of each figure in square units. b) Which figure has the greater area, and by how many square units?
Figure for problem 531715

Hints

- Try splitting each figure into smaller rectangles or squares. - You can also count the unit squares inside each figure. - Subtract the smaller area from the greater area to find the difference.

Solution

1. Figure A can be split into two rectangles. Their areas are \(2 \times 4 = 8\) square units and \(2 \times 2 = 4\) square units, so the total area is \(8 + 4 = 12\) square units. 2. Figure B can also be split into two rectangles. Their areas are \(4 \times 2 = 8\) square units and \(2 \times 3 = 6\) square units, so the total area is \(8 + 6 = 14\) square units. 3. Since \(14 - 12 = 2\), Figure B has the greater area by \(2\) square units.

Answer

a) Figure A has an area of \(12\) square units, and Figure B has an area of \(14\) square units. b) Figure B has the greater area by \(2\) square units.
5165253
A tile installer makes squares from rectangular tiles. Each rectangular tile is \(20\,\text{cm}\) long and \(10\,\text{cm}\) wide. The installer places two tiles together along their long sides to make one square. a) What is the side length of the square? b) The installer wants to cover a square area with side length \(60\,\text{cm}\) using the squares from part a). How many of the squares are needed? c) How many original rectangular tiles are needed altogether?

Hints

- Think about how two rectangles can make a square. - Find how many small-square side lengths fit along one side of the large square. - Remember that the squares form both rows and columns. - Each small square is made from two rectangular tiles.

Solution

1. Placing two \(20\,\text{cm} \times 10\,\text{cm}\) rectangles together along their \(20\,\text{cm}\) sides makes a \(20\,\text{cm} \times 20\,\text{cm}\) square. 2. Along each side of the larger square, \(60 \div 20 = 3\) small squares fit. Therefore, \(3 \times 3 = 9\) small squares are needed. 3. Each small square uses \(2\) rectangular tiles, so \(9 \times 2 = 18\) rectangular tiles are needed.

Answer

a) \(20\,\text{cm}\) b) \(9\) squares c) \(18\) rectangular tiles

All problems may be used, copied and printed free of charge for school and tutoring, including paid tutoring. Commercial adaptations as well as publication or redistribution on the internet are not permitted.

Building free math worksheets