Lesson 10 of 12

▲ Geometry: Area & Perimeter

🎯 Grades 6–8 ⏱ ~35 minutes 🟡 Intermediate

What You'll Learn

Area and perimeter formulas for rectangles, triangles, and circles
The difference between area (square units) and perimeter (linear units)
How to apply these formulas to real-world problems

▲ Shape Area & Perimeter Calculator

Select a shape and adjust its dimensions to see area and perimeter calculated with step-by-step work.

Shape:

Area vs Perimeter

Perimeter is the total distance around the outside of a shape — measured in units (cm, m, ft). Area is the amount of space inside a shape — measured in square units (cm², m², ft²).

Think of perimeter as the length of fence needed around a yard, and area as the amount of grass inside it.

Formulas

Rectangle: A = length × width | P = 2(l + w)

Triangle: A = ½ × base × height | P = side₁ + side₂ + side₃

Circle: A = π × r² | Circumference C = 2πr (≈ 3.14159)

For triangles, the height must be perpendicular to the base — it's not necessarily a side length.

💡

Units Matter!

Always include units in your answer. Area is always in square units (cm², not cm). A common mistake is reporting area in linear units — double-check by asking: "does this answer describe covering a surface?"

🆘

Pi Day

The number π (pi ≈ 3.14159…) is irrational — its decimal goes on forever without repeating. Mathematicians have calculated π to over 100 trillion decimal places! March 14 (3/14) is celebrated worldwide as Pi Day.

❓ Check Your Understanding

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