🧱 See It
Area just means "how many unit squares fit inside." A plain rectangle is the easiest to count — no cutting required:
6 across, 4 up — 24 unit squares fill the rectangle.
Now imagine slanting the rectangle's top so it leans over — that's a parallelogram. Cut a triangle-shaped sliver off the slanted end and slide it to the other side: it snaps back into the exact same plain rectangle. Same base, same height, same number of squares inside — just rearranged.
A triangle is even simpler: two identical triangles pushed together, point to point, make one whole parallelogram. So one triangle is always exactly half of it.
✏️ Draw It
Here's a rectangle, 5 across and 4 up:
5 × 4 = 20 unit squares.
A parallelogram with that same base and height holds the same 20 squares — slide the end triangle over and it becomes this exact rectangle.
A triangle with that same base and height is literally half of this rectangle. Shade half the squares to see it:
10 shaded squares out of 20 — the triangle is half the rectangle, no matter how the diagonal cut actually runs.
Those squares work the same way even once the sides actually slant. Each shape below is real (not just a rectangle) with the unit squares still showing through, and the height marked as a dashed line meeting the base at a right angle (small square marker) — never along a slanted side:
A parallelogram — the top has slid sideways, but the height is still the straight up-and-down distance, not the slanted side.
A triangle — same height marker, but the shape comes to a single point instead of a second base.
A trapezoid — a short base on top, a long base on the bottom, still connected by the same kind of height line.
🔢 Write It
Three shapes, three formulas — but they're all just "fill the inside" in disguise:
Rectangle / Parallelogram Area = base × height
Triangle Area = (base × height) ÷ 2
Trapezoid Area = ((base1 + base2) ÷ 2) × height
💡 Worked Examples
Example 1 — Triangle: base = 8, height = 5
- Formula:
Area = (base × height) ÷ 2 - Plug in:
Area = (8 × 5) ÷ 2 - Multiply:
Area = 40 ÷ 2 - Answer:
Area = 20
Example 2 — Trapezoid: base1 = 6, base2 = 10, height = 4
- Formula:
Area = ((base1 + base2) ÷ 2) × height - Plug in:
Area = ((6 + 10) ÷ 2) × 4 - Add the bases:
Area = (16 ÷ 2) × 4 - Divide:
Area = 8 × 4 - Answer:
Area = 32
🧠 Quick Reference
| Shape | Formula |
|---|---|
| Rectangle / Parallelogram | base × height |
| Triangle | (base × height) ÷ 2 |
| Trapezoid | ((base1 + base2) ÷ 2) × height |