Free Math Worksheets

- Perimeter is the total distance around a figure. - Add the lengths of all four sides. - Include the unit in your answer.

1. Add all four side lengths: \(5 + 4 + 4 + 5 = 18\). 2. The perimeter is \(18\,\text{cm}\).

The perimeter of the quadrilateral is \(18\,\text{cm}\).

- Trace the entire outside boundary of each figure. - Count each horizontal or vertical step between neighboring pegs as \(1\) unit. - Add the boundary lengths, then compare the totals.

1. The perimeter of Figure A is \(4 + 1 + 3 + 2 + 1 + 3 = 14\) units. 2. The perimeter of Figure B is \(1 + 2 + 1 + 1 + 3 + 1 + 1 + 2 = 12\) units. 3. The perimeter of Figure C is \(3 + 1 + 1 + 1 + 1 + 1 + 1 + 3 = 12\) units. 4. Figure A has the greatest perimeter.

Figure A: \(14\) units Figure B: \(12\) units Figure C: \(12\) units Figure A has the greatest perimeter, \(14\) units.

- Perimeter is the distance around the outside of a figure. - Count the unit-length segments between pegs along each boundary. - Add all the boundary lengths before comparing.

1. Figure a) is a rectangle with side lengths \(3\) units and \(2\) units. Its perimeter is \(3 + 2 + 3 + 2 = 10\) units. 2. Tracing Figure b) gives side lengths \(2\), \(1\), \(1\), \(1\), \(1\), and \(2\) units. Its perimeter is \(2 + 1 + 1 + 1 + 1 + 2 = 8\) units. 3. Since \(10 > 8\), Figure a) has the greater perimeter.

Figure a) has a perimeter of \(10\) units. Figure b) has a perimeter of \(8\) units. Figure a) has the greater perimeter.

- Add the number of unit squares in each column. - For perimeter, count every unit-length segment around the outside boundary.

1. The four columns have heights \(4\), \(3\), \(2\), and \(1\). The area is \(4 + 3 + 2 + 1 = 10\) square units. 2. The bottom and left sides are each \(4\) units long. The stepped boundary has four horizontal unit segments and four vertical unit segments. The perimeter is \(4 + 4 + 4 + 4 = 16\) units.

a) \(10\) square units b) \(16\) units

- How many sides does a square have? - Are all the sides of a square the same length? - How can you find the total distance around the outside edge?

1. A square has four sides of equal length. 2. Add the lengths of all four sides: \(P = 4 \times 70\,\text{cm}\). 3. Therefore, \(P = 280\,\text{cm}\).

\(280\,\text{cm}\) of lace trim is needed.

- Multiply the number of rows by the number of columns to find the area. - Only the outside edges count toward the perimeter.

1. The area is the number of tiles: \(5 \times 8 = 40\) tiles. 2. The rectangle has two sides of length \(8\) and two sides of length \(5\). Its perimeter is \(2 \times 8 + 2 \times 5 = 26\) tile-side lengths.

Area: \(40\) tiles Perimeter: \(26\) tile-side lengths

- Count the unit squares inside each figure to find its area. - To find perimeter, trace the entire outside boundary and count each unit-length segment. - Be sure to count the inward and outward segments of Figure C.

1. Figure A is a \(4 \times 2\) rectangle, so its area is \(8\) square units. 2. Counting or decomposing Figure B gives an area of \(8\) square units. 3. Counting or decomposing Figure C gives an area of \(8\) square units. Therefore, all three figures have the same area. 4. The perimeter of Figure A is \(4 + 2 + 4 + 2 = 12\) units. 5. The perimeter of Figure B is \(5 + 1 + 2 + 1 + 3 + 2 = 14\) units. 6. The perimeter of Figure C is \(4 + 3 + 1 + 2 + 2 + 2 + 1 + 3 = 18\) units. 7. Figure C has the greatest perimeter.

a) Each figure has an area of \(8\) square units. b) Figure A: \(12\) units Figure B: \(14\) units Figure C: \(18\) units Figure C has the greatest perimeter.

- Count the unit squares inside each figure to find area. - Trace the entire boundary and count each unit-length segment to find perimeter. - Compare the areas separately from the perimeters.

1. Rectangle 1 has \(4\) unit squares in each of \(3\) rows, so its area is \(4 + 4 + 4 = 12\) square units. 2. Figure 2 has \(4\) unit squares in the bottom row, \(1\) in the middle row, and \(4\) in the top row, so its area is \(4 + 1 + 4 = 9\) square units. 3. The perimeter of Rectangle 1 is \(4 + 3 + 4 + 3 = 14\) units. 4. Adding the boundary lengths of Figure 2 gives \(4 + 1 + 3 + 1 + 3 + 1 + 4 + 3 = 20\) units. 5. Rectangle 1 has the greater area, while Figure 2 has the greater perimeter.

a) Rectangle 1 has an area of \(12\) square units. Figure 2 has an area of \(9\) square units. Rectangle 1 has the greater area. b) Figure 2 has the greater perimeter: \(20\) units compared with \(14\) units for Rectangle 1.

- Equal areas do not always have equal perimeters. - Add two lengths and two widths for each rectangle.

1. The \(3 \times 8\) rectangle has perimeter \(2 \times 3 + 2 \times 8 = 22\) tile-side lengths. 2. The \(4 \times 6\) rectangle has perimeter \(2 \times 4 + 2 \times 6 = 20\) tile-side lengths. 3. The \(4 \times 6\) rectangle has the smaller perimeter.

The \(4 \times 6\) rectangle has the smaller perimeter: \(20\) tile-side lengths. The \(3 \times 8\) rectangle has a perimeter of \(22\) tile-side lengths.