Middle School Number Sense Lesson 42: Rectangles
Most mathletes have been working with rectangles since we were little. We learned the formulas for the area and perimeter of a rectangle soon after we mastered squares. For number sense purposes, area and perimeter are the main concepts dealing with rectangles--which is pretty basic. But we will see a little more complexity in rectangle questions--especially on high school tests. This concept appeared 11 times in middle school this year, with a median placement at question # 36.
Number Dojo Level: 147
Let's review the formulas for area and perimeter. L stands for length and W stands for width.
Example 1: The area of a rectangle with length 22 and width 18 is ___
Example 2: If the area of a rectangle is 42 and the length is 10, then the width is ___
Example 3: Find the length of a rectangle with perimeter 48 and width 8.
Example 4: The area of a rectangle is 160. If its length is 16, then its perimeter is ___
Example 5: If a rectangle of area 40 has width 5, then the perimeter of the rectangle is ___
Example 6: Find the ratio of the perimeter of a 3" x 6" rectangle to its area. ___
Another concept related to rectangles deals with right triangles. (If you draw one diagonal of a rectangle, the diagonal divides the rectangle into two identical right triangles). The Pythagorean Theorem states that for right triangles:
Most mathletes have been working with rectangles since we were little. We learned the formulas for the area and perimeter of a rectangle soon after we mastered squares. For number sense purposes, area and perimeter are the main concepts dealing with rectangles--which is pretty basic. But we will see a little more complexity in rectangle questions--especially on high school tests. This concept appeared 11 times in middle school this year, with a median placement at question # 36.
Number Dojo Level: 147
Let's review the formulas for area and perimeter. L stands for length and W stands for width.
- Area: L x W
- Perimeter: 2(L + W)
Example 1: The area of a rectangle with length 22 and width 18 is ___
- Area = L x W = 22 x 18.
- Using DiffSquares1, 22 x 18 = 396.
Example 2: If the area of a rectangle is 42 and the length is 10, then the width is ___
- Area = L x W. 42 = 10 x W.
- W = 42 ÷ 10 = 4.2.
Example 3: Find the length of a rectangle with perimeter 48 and width 8.
- Perimeter = 2(L + W). 48 = 2(L + 8).
- 48 = 2L + 16, so 2L = 48 - 16 = 32.
- 2L = 32, so L = 16.
Example 4: The area of a rectangle is 160. If its length is 16, then its perimeter is ___
- Area = L x W. 160 = 16 x W. W = 160 ÷ 16 = 10.
- Perimeter = 2(L + W) = 2(16 + 10) = 2(26) = 52.
Example 5: If a rectangle of area 40 has width 5, then the perimeter of the rectangle is ___
- Area = L x W. 40 = L x 5. L = 40 ÷ 5 = 8.
- Perimeter = 2(L + W) = 2(8 + 5) = 2(13) = 26.
Example 6: Find the ratio of the perimeter of a 3" x 6" rectangle to its area. ___
- Area = L x W = 6 x 3 = 18.
- Perimeter = 2(L + W) = 2(6 + 3) = 2(9) = 18.
- Ratio = Perimeter ÷ Area = 18 ÷ 18 = 1.
Another concept related to rectangles deals with right triangles. (If you draw one diagonal of a rectangle, the diagonal divides the rectangle into two identical right triangles). The Pythagorean Theorem states that for right triangles:
Or, if you think in terms of the parts of the rectangle, with D representing the diagonal,
Example 7: Find the diagonal of a rectangle with length 15 and width 8.
1. D2 = L2 + W2 = 152 + 82.
2. D2 = 225 + 64 = 289.
3. D = 17.
Here's a free worksheet to help you practice Rectangle:
| rectangle.pdf |
Up Next for Middle School: Trapezoid
RSS Feed
