Lesson 5.95.9 Small Group · Group 1
Group 1 · Set BSecond form · new problems, same idea
Learning target With my small group, I can find the area of a regular polygon by decomposing it into triangles — one step at a time, with support.
Remember5.9 Small Group · Group 1
The area of a regular polygon is the area of one center triangle times the number of sides. A regular polygon splits into equal triangles from its center. Find one triangle, then multiply by the number of sides.
Words: Regular Polygon (Polígono regular)Decompose (Descomponer)Triangle (Triángulo)Composite (Compuesto)Formula (Fórmula)
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1Complete each step, then write the final answer.
A regular octagon splits into 8 equal triangles. Each triangle has a base of 5 in and a height of 6 in. Find the area of the octagon.
Show your workHint One triangle: 1/2 × 5 × 6 = 15. There are 8 triangles.
Final answer: -
2Complete each step, then write the final answer.
A regular decagon has 10 sides of 2 cm. Each center triangle has a height of 3.1 cm. Estimate the area.
Show your workHint Find one triangle. Then multiply by the number of sides.
Final answer: -
3Complete each step, then write the final answer.
A floor tile is a regular hexagon. Each side is 2 in. Each center triangle has a height of 1.7 in. About how much floor does one tile cover?
Show your workHint The floor a tile covers is its area. Split the hexagon into triangles from the center.
Final answer: -
4Complete each step, then write the final answer.
A regular polygon is split into equal center triangles. Each triangle has an area of 12 square centimeters. The polygon's area is 96 square centimeters. How many sides does it have?
Show your workHint How many 12s make 96? Each triangle sits on one side.
Final answer:
Explain your thinkingWhy do we multiply one triangle's area by the number of sides? Use Leo's hexagon to explain.
Sentence starter There is one triangle for each ___. · Leo's answer is double because ___.