Lesson 2 — Squares and Rectangles
Big idea: A rectangle’s area is its base times its altitude, and a square is simply a rectangle whose base and altitude are equal.
Words to know
| Word | Meaning |
|---|---|
| Rectangle | A quadrilateral with four right angles. |
| Square | A rectangle with all four sides equal. |
| Base | One side of a rectangle; any side may be chosen as the base. |
| Altitude (height) | A side perpendicular to the base. |
| Dimensions | The length and width (base and altitude) of a rectangle. |
| Perimeter | The distance around a figure; add the side lengths. |
Concepts to know
- The dimensions of a rectangle are also called its base and altitude.
- Any side can be the base, and a side perpendicular to it is the altitude.
- Postulate 9: The area of a rectangle is the product of its base and altitude.
- Corollary to Postulate 9: The area of a square is the square of its side.
- The rectangle formula is assumed to work for all rectangles, including those whose dimensions are not whole numbers.
- A square is a special rectangle, so its formula follows from Postulate 9.
Formulas / rules
- Rectangle: A = bh (base × altitude)
- Square: A = s² (side × side)
- Rectangle perimeter: P = 2b + 2h
- Square perimeter: P = 4s
- Units: area in square units, perimeter in linear units.
Homework helper
| If the homework asks… | Do this… |
|---|---|
| Find the area of a rectangle | Multiply base by altitude; make sure the units match. |
| Find the area of a square | Square the side length. |
| Find a missing side | Substitute into A = bh or A = s² and solve. |
| Find the cost to cover a surface | Find the area, then multiply by the cost per square unit. |
| Compare a square and a rectangle | Compute both areas; equal areas do not require equal perimeters. |
| Find perimeter | Add all four sides, or use P = 2b + 2h. |
Watch out
- Base and altitude must be perpendicular; do not multiply two slanted sides.
- Area uses square units; perimeter uses linear units.
- A rectangle with the same perimeter as another can have a different area.
- “Height” means altitude, not a slanted side length.