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🔷 Polygon Angles, Area, and Volume

Add up the angles inside any polygon, measure the area of flat shapes, and calculate the volume of solids — three powerful geometry tools in one course.

3
lessons
~30 min
to learn
🔢 Math
subject
Teens
level
Start the course →

What you’ll learn

  1. Angles Inside PolygonsCalculate interior and exterior angle sums of polygons and the angles of regular polygons.A polygon is a closed shape with straight sides. Splitting it into triangles from one corner shows that its interior angles total (n − 2) × 180°: 360° for a quadrilateral, 540° for a pentagon, and so on. In a regular polygon all angles are equal, so divide the total by n. The exterior angles of any polygon always add up to 360°.
  2. Finding AreaCalculate the area of rectangles, triangles, and related shapes using their formulas.Area measures the flat space inside a shape, counted in square units. A rectangle's area is length × width, and a triangle's is ½ × base × height because a triangle is half its surrounding rectangle. A parallelogram uses base × height. Matching each shape to the right formula lets you find its area quickly.
  3. Measuring VolumeCalculate the volume of cuboids using length × width × height.Volume measures the space a solid fills, counted in cubic units like cm³. For a cuboid, cover the base with unit cubes (length × width) and stack that layer up by the height, giving volume = length × width × height. A 4 × 3 × 2 box holds 24 cm³. These same ideas extend to any prism.

Questions this course answers

What is the sum of the interior angles of a pentagon (5 sides)?

A pentagon splits into 3 triangles, so its angle sum is (5 − 2) × 180 = 540°.

What is each interior angle of a regular pentagon?

The angles total 540° and are shared equally among 5 corners: 540 ÷ 5 = 108°.

The exterior angles of any polygon add up to what total?

Walking once around a polygon is one full turn, so the exterior angles always total 360°.

What does area measure?

Area is the amount of flat space inside a shape, measured in square units.

A rectangle is 8 cm long and 5 cm wide. What is its area?

Rectangle area is length × width, so 8 × 5 = 40 cm².

A triangle has base 6 cm and height 4 cm. What is its area?

Triangle area is ½ × base × height = ½ × 6 × 4 = 12 cm².

Grounded in trusted sources

  • Khan Academy — area, volume, and polygon angles
  • National Council of Teachers of Mathematics
  • BBC Bitesize — area and volume
  • Britannica — polygon

Every Wunder lesson is built from real, reputable sources — never invented.

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