Free Printable WorksheetMathGeometryMath CurriculumG-MG.A.2-3

GEO.175 Use geometry to design under constraints Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Geometry Math worksheet provides structured practice on GEO.175 Use geometry to design under constraints. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

GEO.175 Use geometry to design under constraints - Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.2-3. Skill statement in this prompt cell: Select the design option that satisfies the geometric constraints and yields the stated objective (such as minimal surface area). Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.2-3; FL MA.912.GR.4.4-4.5; MA G-MG.A.2-3. 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.175 Use geometry to design under constraints skill assessments:

Problem 1Difficulty: Mastery

A community garden can be a rectangle, circle, regular hexagon, or square. It must enclose at least 300 square feet and use no more than 70 feet of border. Which design gives the greatest area?

ARectangle 15 ft by 20 ft

BCircle with radius 10 ft

CRegular hexagon with side 10 ft

DSquare with side 18 ft

Solution & Explanation:The regular hexagon area is about 259.8, so it is too small. The square has perimeter 72, so it fails the border limit. The rectangle has area 300 and border 70. The circle has area about 314 and border about 62.8, so option B gives the greatest valid area.

Problem 2Difficulty: Mastery

A closed triangular-prism package has a right-triangle cross-section and must hold at least 240 cubic inches. Which option uses the least material?

ARight-triangle legs 6 in and 8 in, length 10 in

BRight-triangle legs 5 in and 12 in, length 8 in

CRight-triangle legs 8 in and 15 in, length 4 in

DRight-triangle legs 7 in and 24 in, length 3 in

Solution & Explanation:All four options have volume at least 240 cubic inches. Surface area is 2(triangle area) plus prism length times the triangle perimeter. The surface areas are 288, 300, 280, and 336 square inches. Option C is least.

Problem 3Difficulty: Mastery

A rectangular garden is built against a wall, so fencing is needed for only three sides. The fence budget is 120 feet, and the goal is the greatest possible area. Which design should be selected?

A60 ft along the wall and 30 ft out from the wall

B70 ft along the wall and 25 ft out from the wall

C50 ft along the wall and 35 ft out from the wall

D80 ft along the wall and 20 ft out from the wall

Solution & Explanation:Fencing is L + 2W. All choices use 120 feet or less. The areas are 1800, 1750, 1750, and 1600 square feet. Option A gives the greatest area.

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Frequently Asked Questions

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QHow do I download and print this GEO.175 Use geometry to design under constraints worksheet?

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QIs this GEO.175 Use geometry to design under constraints 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-MG.A.2-3 (Primary standard selected for prompt fields in this prompt cell: CCSS G-MG.A.2-3. Skill statement in this prompt cell: Select the design option that satisfies the geometric constraints and yields the stated objective (such as minimal surface area). Associated standards listed with this skill in the curriculum source: CCSS G-MG.A.2-3; FL MA.912.GR.4.4-4.5; MA G-MG.A.2-3. Use this prompt-provided wording as the supporting standard description for this workflow.).