📏 Perimeter & Area – Quick Study Notes
(For the NMMS Mathematics SAT section)
1. What is Perimeter?
- Perimeter = the total length around a shape.
- Think of it as the “border walk” you’d take if you walked all the way around a picture.
- Units are the same as the side lengths (cm, m, inches, etc.).
How to Find It
- Add all the side lengths together.
- If some sides are equal, just multiply that side by how many times it appears.
Tiny Example
A rectangle has sides 4 cm and 7 cm.
Perimeter = 4 + 4 + 7 + 7 = 22 cm.
2. What is Area?
- Area = the amount of flat surface inside a shape.
- Imagine filling the shape with square tiles of size 1 unit × 1 unit.
- Units are square (cm², m², in², etc.).
How to Find It
| Shape | Formula (very simple) | Tiny Example |
|---|---|---|
| Rectangle | length × width | 5 m × 3 m = 15 m² |
| Square | side × side | 4 in × 4 in = 16 in² |
| Triangle | ½ × base × height | 6 cm × 4 cm = 12 cm² (½ × 6 × 4) |
| Circle | π × radius² | radius 3 cm → 3.14 × 3² ≈ 28.26 cm² |
- For a circle, π ≈ 3.14.
3. Step‑by‑Step: Find the Perimeter of a Triangle
- Identify the three side lengths.
- Add them together.
Example
Sides: 5 cm, 7 cm, 8 cm.
Perimeter = 5 + 7 + 8 = 20 cm.
4. Step‑by‑Step: Find the Area of a Circle
- Find the radius (half of the diameter).
- Square the radius (multiply it by itself).
- Multiply by π (≈3.14).
Example
Diameter = 10 cm → radius = 5 cm.
Area = 3.14 × 5² = 3.14 × 25 = 78.5 cm².
5. Quick Tips
- Remember units: perimeter → same units as sides; area → square units.
- For a regular polygon (all sides equal), perimeter = side × number of sides.
- For shapes you can break into simpler parts (e.g., an L‑shape = two rectangles), find each area and add them.
6. Mini Practice Problems
-
A rectangle is 9 m long and 4 m wide.
- Find the perimeter.
- Find the area.
-
A triangle has sides 3 cm, 4 cm, 5 cm.
- Find the perimeter.
- If the height from the base of 5 cm is 2.4 cm, find the area.
-
A circle’s radius is 6 inches.
- Find the area (use π = 3.14).
- Find the circumference (use 2πr).
(Try solving them before checking the answers below.)
7. Answers
-
Perimeter = 9 + 9 + 4 + 4 = 26 m.
Area = 9 × 4 = 36 m². -
Perimeter = 3 + 4 + 5 = 12 cm.
Area = ½ × 5 × 2.4 = 6 cm². -
Area = 3.14 × 6² = 3.14 × 36 = 113.04 in².
Circumference = 2 × 3.14 × 6 = 37.68 in.
8. Final Thought
- Perimeter is the “walk around” length.
- Area is the “tiles you need” to cover the inside.
- Once you remember the basic formulas, you can tackle most SAT geometry problems quickly and confidently.
Happy studying! 🚀