Area of Polygons

Section 2.5 Area of Polygons

\(\textbf{Why polygons?}\)

The \(\textbf{area of a polygon }\) refers to the amount of space enclosed within its boundaries. It is measured in square units e.g., cm², m², in² etc.

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Activity 2.5.1.

\(\textbf{Materials needed:}\)

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Sticks (e.g. matchsticks, toothpicks, broom straws, twigs)
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Thread, string, rubber bands, or yarn
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Recycled cardboard, cereal boxes, or packaging paper
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Bottle caps or buttons (as vertices)
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Scissors
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Glue or tape \(\textbf{(d)}\)
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Ruler and protractor (if available)
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Have you seen shapes with straight sides around you?
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What do you think makes a shape a polygon?
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In pairs or small groups, create physical models of different polygons using the available materials.
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Using sticks \(\textbf{(a)}\) or straws for sides and caps\(\textbf{(c)}\) or buttons for vertices
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Use sticks or straws for sides and caps or buttons for vertices as shown alongside.
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(a) Construct at least:
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(b) A triangle
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(c) A quadrilateral
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(d) A pentagon
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(e) A hexagon
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Present what type of polygon each model is and how many sides/vertices it has.
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“What’s common in all these shapes?”
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“What’s the minimum number of sides a polygon can have?”
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\(\textbf{Key Takeaway}\)

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♦ A \(\textbf{polygon}\) is a closed two dimension formed by straight lines that connect end to end at a point called a \(\textbf{vertex}\text{.}\) Examples of polygons include triangles, quadrilaterals, pentagons, hexagons, heptagons,octagons, nonagons and decagons. \(\textbf{Their sides do not curve or overlap.}\)

Note that most of the interior angles of a polygon are smaller than exterior angles.
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\(\textbf{Types of Polygons} \)
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We have different types of polygons but we are going to focus on only two in this chapter Regular polygons and irregular polygons.
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🔹 Regular polygons – All sides and angles are equal (e.g., square, equilateral triangle).
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🔹 Irregular polygons – Sides and angles are not equal (e.g., a scalene triangle, a random quadrilateral).
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🔹 Convex polygons – All interior angles are less than 180°.
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🔹 Concave polygons – At least one interior angle is greater than 180°.
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Why is Area Important?

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Would you wish to pursue a career some day? Have you ever seen an Architect?

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So finding area is Essential in design and architecture as well as construction of houses for it helps to determine the spacing of rooms in a house in relation to the effect desired.

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