Free Printable WorksheetMathGeometryMath CurriculumG-GMD.B.4

GEO.155 Area and perimeter of polygons and compound figures Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.155 Area and perimeter of polygons and compound figures. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.155 Area and perimeter of polygons and compound figures - Primary standard selected for prompt fields in this prompt cell: CCSS G-GMD.B.4. Skill statement in this prompt cell: Select the correct formula or decomposition and compute the area or perimeter of a polygon or compound figure. 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-GPE.B.7; FL MA.912.GR.3.4; MA G-GPE.B.7; NY GEO G.G-GPE.B.7. 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.155 Area and perimeter of polygons and compound figures skill assessments:

Problem 1Difficulty: Mastery
A community mural is made of a 24-foot by 10-foot rectangle, a trapezoid on top with bases 24 feet and 16 feet and height 5 feet, and two right triangles attached to the sides. Each triangle has legs 4 feet and 10 feet. Paint covers 120 square feet per gallon. How many whole gallons are needed for one coat?
A3 gallons
B4 gallons
C5 gallons
D6 gallons
Solution & Explanation:The rectangle area is 24 * 10 = 240. The trapezoid area is 1/2 * (24 + 16) * 5 = 100. The two triangles add 2 * (1/2 * 4 * 10) = 40. Total area is 380, and 380 / 120 rounds up to 4 gallons.
Problem 2Difficulty: Mastery
A 21-foot by 15-foot rectangle has a 9-foot by 6-foot rectangle attached along the 9-foot side. What are the area and perimeter of the compound figure?
AArea 369 square feet; perimeter 84 feet
BArea 369 square feet; perimeter 102 feet
CArea 315 square feet; perimeter 84 feet
DArea 261 square feet; perimeter 72 feet
Solution & Explanation:Area adds because there is no overlap: 21 * 15 + 9 * 6 = 315 + 54 = 369. Perimeter is 2(21 + 15) + 2(9 + 6) - 2(9) = 72 + 30 - 18 = 84.
Problem 3Difficulty: Mastery
A regular decagon has side length 8 units and apothem 12 units. Which pair gives its perimeter and area?
APerimeter 80 units; area 480 square units
BPerimeter 96 units; area 480 square units
CPerimeter 80 units; area 960 square units
DPerimeter 40 units; area 240 square units
Solution & Explanation:A decagon has 10 equal sides, so the perimeter is 10 * 8 = 80. Area is 1/2 * apothem * perimeter = 1/2 * 12 * 80 = 480 square units.

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Frequently Asked Questions

Common questions about printing, using, and solving this worksheet

QHow do I download and print this GEO.155 Area and perimeter of polygons and compound figures worksheet?

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QIs this GEO.155 Area and perimeter of polygons and compound figures 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 formula or decomposition and compute the area or perimeter of a polygon or compound figure. 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-GPE.B.7; FL MA.912.GR.3.4; MA G-GPE.B.7; NY GEO G.G-GPE.B.7. Use this prompt-provided wording as the supporting standard description for this workflow.).

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