Free Printable WorksheetMathGeometryMath CurriculumG-GMD.B.4

GEO.157 Area of regular polygons Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.157 Area of regular polygons. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.157 Area of regular polygons - Primary standard selected for prompt fields in this prompt cell: CCSS G-GMD.B.4. Skill statement in this prompt cell: Select the correct method and compute the area of a regular polygon using its apothem and perimeter (or its side length). Associated standards listed with this skill in the curriculum source: CCSS G-GMD.B.4; FL MA.912.GR.4.1-4.2; VA G.DF.1a; CCSS G-CO.C.10; FL MA.912.GR.1.3; MA G-CO.C.10; NY GEO G.G-CO.C.10; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.

Whether you are an educator preparing classroom handouts, a tutor reinforcing weekly topics, or a parent supporting homeschool learning, this printable resource gives students the deliberate practice required to achieve subject fluency and master state standards.

Grade

Geometry

Subject

Math

Domain

Math Curriculum

Formats

PDF & DOCX

Sample Practice Problems

Preview the types of problems and questions covered in this worksheet

Below are sample questions representative of the exercises included on this worksheet and related GEO.157 Area of regular polygons skill assessments:

Problem 1Difficulty: Mastery
A regular polygon has side length 12 units, apothem 10 units, and area 360 square units. What type of regular polygon is it?
ARegular triangle
BRegular pentagon
CRegular hexagon
DRegular decagon
Solution & Explanation:Let n be the number of sides. The area is A = 1/2 * 10 * (12n) = 60n. Since 60n = 360, n = 6, so the polygon is a regular hexagon.
Problem 2Difficulty: Mastery
A regular decagonal pond cover has side length 1.6 meters and apothem 2.45 meters. Fabric costs $18 per square meter. What is the fabric cost?
A$176.40
B$352.80
C$705.60
D$18.00
Solution & Explanation:The perimeter is 10 * 1.6 = 16 meters. The area is 1/2 * 2.45 * 16 = 19.6 square meters. The cost is 19.6 * $18 = $352.80.
Problem 3Difficulty: Mastery
A student knows a regular polygon's side length but not its perimeter. Which additional information is needed to apply the regular-polygon area formula from side length?
AThe polygon's color and orientation
BThe number of sides and the apothem
COnly the final area
DOnly the perimeter, with no apothem
Solution & Explanation:From side length, the number of sides is needed to find the perimeter. The apothem is also needed for A = 1/2(apothem)(perimeter).

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Frequently Asked Questions

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QIs this GEO.157 Area of regular polygons worksheet free for teachers and homeschoolers?

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Geometry Math students. It aligns with educational standard G-GMD.B.4 (Primary standard selected for prompt fields in this prompt cell: CCSS G-GMD.B.4. Skill statement in this prompt cell: Select the correct method and compute the area of a regular polygon using its apothem and perimeter (or its side length). Associated standards listed with this skill in the curriculum source: CCSS G-GMD.B.4; FL MA.912.GR.4.1-4.2; VA G.DF.1a; CCSS G-CO.C.10; FL MA.912.GR.1.3; MA G-CO.C.10; NY GEO G.G-CO.C.10; TEKS §111.41(c). Use this prompt-provided wording as the supporting standard description for this workflow.).

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