Area and Perimeter Summary

Geometry · Axiom Academy

SUMMARY Unit 6 Summary: Area & Perimeter Everything we measured about flat shapes — the space inside (area) and the distance around (perimeter), from rectangles to circles to composite figures. Area is the space inside a shape (square units); perimeter is the distance around its boundary (linear units). Every straight-sided area formula traces back to the rectangle A = lw — a triangle is half a rectangle, a parallelogram is a rectangle that's been sheared. For triangles and parallelograms, h is the perpendicular height to the base — never the slant side. A circle has two measures: area and circumference . Halve a diameter to get the radius first. Composite figures have no single formula — break them into simple regions and add or subtract . Core Concept Rectangle: Area & Perimeter The foundation of all area work. Counting unit squares in a grid of l columns and w rows gives . The perimeter is the two lengths plus the two widths. When to use: any four-sided figure with right angles (a square is the l = w case). Watch out for: area is in square units, perimeter in plain units — don't mix them. A triangle is exactly half of a rectangle (or parallelogram) on the same base and height — so its area is half of bh . Any side can be the base, as long as h is measured to it. When to use: any triangle, given a base and the height to it. Watch out for: h is the perpendicular height ( to the base), not the length of a slanted side. Core Concept Parallelogram Area

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