Perimeter, Area and Circles: Class 7 Study Guide
Perimeter is the distance around a shape and area is the space inside it.
The perimeter is the length of the boundary. For a rectangle it is 2(l + b), for a square 4a. The area is measured in square units. For a rectangle it is l ร b, for a square aยฒ, for a triangle ยฝ ร base ร height and for a parallelogram base ร height.
A circle has radius r and diameter d = 2r. Its perimeter is called the circumference, C = 2ฯr, and its area is A = ฯrยฒ. Use ฯ = 22/7 or 3.14.
Formulas
| Shape | Perimeter | Area |
|---|---|---|
| Rectangle | 2(l + b) | l ร b |
| Square | 4a | aยฒ |
| Triangle | sum of sides | ยฝ ร b ร h |
| Parallelogram | 2(a + b) | b ร h |
| Circle | 2ฯr | ฯrยฒ |
A worked circle
A circle has radius 7 cm. Circumference = 2 ร 22/7 ร 7 = 44 cm, and area = 22/7 ร 7 ร 7 = 154 cmยฒ. A circular garden of radius 14 m has an area of 22/7 ร 14 ร 14 = 616 mยฒ.
C or A.
Use the radius, not the diameter.
With ฯ = 22/7 or 3.14.
cm, mยฒ and so on.
Composite shapes
To find the area of a shape made from simpler shapes, split it, find each area and add or subtract. A path around a rectangular garden is found by subtracting the garden's area from the larger area including the path.
Worked examples and common mistakes
Example: A triangle has base 10 cm and height 6 cm. Area = 30 cmยฒ. Example: A parallelogram with base 8 cm and height 5 cm has area 40 cmยฒ. Common mistakes: using the diameter as the radius, using a slanted side as the height, and mixing units. The height must be perpendicular to the base.
Check your understanding: model answers
1. 22/7 ร 21 ร 21 = 1,386 cmยฒ. 2. 26 cm. 3. 54 = ยฝ ร 12 ร h, so h = 9 cm.
โจ Key Takeaways
- Perimeter is the boundary and area is the space inside.
- Area of a triangle is ยฝ ร base ร height.
- Circle: C = 2ฯr and A = ฯrยฒ.
- Area uses square units.
๐ฌ Questions for Discussion & Reflection
- Find the area of a circle of radius 21 cm (ฯ = 22/7).
- Find the perimeter of a rectangle 9 cm by 4 cm.
- A triangle has base 12 cm and area 54 cmยฒ. Find its height.