Lesson 9: Area of Regular Polygons6.GR.1

I can…

I can find the area of a regular polygon by decomposing it into triangles.

Key words

• Area of Regular Polygons — Split it into equal triangles, then add their areas.
• Regular Polygon — A closed shape with equal sides and equal angles.
• Decompose — Break a number or shape into smaller parts.
• Triangle — A shape with three sides.
• Composite — Made of two or more simple shapes.
• Formula — A rule written with letters and numbers.

Steps

1. My hexagon has 6 equal sides. Each side is 6 feet, and each center triangle has a height of 5.2 feet. Use the rounded height to estimate the area.
2. First I find one triangle: A = ½ × base × height = ½ × 6 × 5.2.
3. I multiply: 6 × 5.2 = 31.2, then ½ × 31.2 = 15.6 square feet.
4. A hexagon has 6 sides, so it has 6 equal triangles.
5. I multiply: 6 × 15.6 = 93.6. So the total area is 93.6 square feet.

Try it

A tabletop shaped like a regular hexagon is decomposed into 6 triangles from its center. Each triangle has a base of 10 inches and a height of 8.7 inches. What is the total area of the tabletop? Use the given rounded height to estimate the area.

Check your answer

261 sq in

One triangle: A = 1/2 x 10 x 8.7 = 43.5 sq in. Total = 6 x 43.5 = 261 square inches.

Sentence starter

I know ___ because ___.

Goal: I can explain my steps using the words regular polygon, decompose, triangle, and composite.