Stuck? Start here. Read the steps, try the problem, then check your answer.
I can…
I can find the area of a regular polygon by decomposing it into triangles.
Key words
Area of Regular Polygons — The space a regular polygon covers. Split it from the center into identical triangles, find one triangle's area, then multiply by how many there are.
Regular Polygon — A closed flat shape made of straight sides, where every side is the same length and every angle is the same size.
Decompose — To break a shape into smaller, simpler shapes.
Triangle — A shape with three sides.
Composite — Made by putting two or more simple shapes together.
Formula — A math rule written with symbols.
Steps
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.
First I find one triangle: A = ½ × base × height = ½ × 6 × 5.2.
I multiply: 6 × 5.2 = 31.2, then ½ × 31.2 = 15.6 square feet.
A hexagon has 6 sides, so it has 6 equal triangles.
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.