Area of Triangles, Parallelograms & Trapezoids: Middle School Geometry

This area of triangles, parallelograms and trapezoids worksheet has students work out why each formula is true before they use it. On printed grid shapes, they cut and move part of a parallelogram to make a rectangle, then join two copies of a triangle, and two copies of a trapezoid, to make a parallelogram. From each drawing they write the area formula themselves.

After the discovery pages, students compare the three proofs, explain why two formulas include one half, and describe in words how a drawing proves a formula. Practice follows with triangles (including one whose height falls outside the shape), a parallelogram with a slanted side to ignore, and two trapezoids, using whole-number and decimal measurements in inches and feet.

Later pages ask students to reason and apply: compare a rectangle, parallelogram and triangle with the same base and height, find the mistake in a student's triangle work, split a house-shaped garden bed into two shapes, work backwards from an area to a missing height or base, and draw their own shapes with a given area.

What's included: 5 student pages and a 2-page answer key.

• Page 1: discover the parallelogram and triangle formulas on grids
• Page 2: discover the trapezoid formula, compare the three proofs and explain one in words
• Page 3: find the area of two triangles, a parallelogram and two trapezoids, with a height and units tip
• Page 4: same base and same height, find the mistake, and a Which formula? challenge
• Page 5: work backwards to a missing measurement and make your own shapes
• Answer key with every answer, pictures showing why each formula works, a model explanation and common mix-ups to watch for

Grades: written for grades 6 and 7 geometry.

Formats: print it in color or in ink-saving black and white.