Free Printable WorksheetMathGrade 6Math CurriculumCCSS 6.G.A.1

6.81 Derive and Use the Area Formula for Triangles Worksheet

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Worksheet Overview & Skills Covered

Core academic competencies and curriculum alignment

This Grade 6 Math worksheet provides structured practice on 6.81 Derive and Use the Area Formula for Triangles. Students are guided through targeted exercises that build foundational understanding, computational accuracy, and critical thinking skills.

Which answer choice correctly uses the triangle area formula (or a valid decomposition) to find the area? (CCSS 6.G.A.1; CA 6.G.A.1; MA 6.G.A.1; NY NY-6.G.1; TX 19 TAC §111.26(b)(8)(B)-(D); FL MA.6.GR.2.1-2.2; VA 6.MG.2a-b)

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

Grade 6

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 6.81 Derive and Use the Area Formula for Triangles skill assessments:

Problem 1Difficulty: Mastery

A triangular roof truss has a base of 32 ft and a perpendicular height of 9.25 ft. Which answer choice correctly finds its area?

A32 x 9.25 = 296 square feet

B1/2 x (32 + 9.25) = 20.625 square feet

C32 + 9.25 = 41.25 square feet

D1/2 x 32 x 9.25 = 148 square feet

Solution & Explanation:Use the triangle area formula A = 1/2 x base x height. Here, 1/2 x 32 x 9.25 = 148, so the area is 148 square feet.

Problem 2Difficulty: Mastery

A stained-glass triangle is made from two triangular pieces with the same height of 6.5 in. The base lengths are 8 in and 5 in. Which answer choice correctly finds the total area?

A8 x 6.5 + 5 x 6.5 = 84.5 square inches

B1/2 x (8 + 5 + 6.5) = 9.75 square inches

C1/2 x 8 x 6.5 + 1/2 x 5 x 6.5 = 42.25 square inches

D1/2 x 8 x 5 = 20 square inches

Solution & Explanation:The two smaller triangles share height 6.5. Add their areas, or use the total base 13: 1/2 x 13 x 6.5 = 42.25 square inches.

Problem 3Difficulty: Mastery

On a map grid, a triangle has a base of 9 grid units and a height of 5 grid units. Each grid unit represents 2 miles. Which answer choice correctly finds the actual area?

A1/2 x 9 x 5 = 22.5 square miles

B1/2 x 18 x 10 = 90 square miles

C18 x 10 = 180 square miles

D1/2 x (18 + 10) = 14 square miles

Solution & Explanation:Convert grid lengths using the scale: the base is 18 and the height is 10. Then 1/2 x 18 x 10 = 90 square miles.

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Frequently Asked Questions

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QWhat grade level and standards does this worksheet align with?

This worksheet is designed specifically for Grade 6 Math students. It aligns with educational standard CCSS 6.G.A.1 (Derive and Use the Area Formula for Triangles).