Formulas: 2D Shapes [TEKS Tools Grade 7]

This post specifically looks at how formulas can be used solve problems involving composite figures and circle geometry. Read more about TEKS Tools and their rationale here.

Formulas

Formulas account for around 22% of each 7th grade STAAR test. These formulas are applied to solve problems related to volume, surface area, composite figures, linear relationships, and composite figures.

The main function of a formula is to understand the relationship between quantities. In fourth grade, students were first introduced to the formulas for area and perimeter of squares and rectangles. In fifth grade, they were introduced to the formula for volume of a rectangular prism. In sixth grade, the formulas for area of a triangle, parallelogram, and trapezoid are explored. For the first time in 7th grade, students are introduced to circle geometry, exploring π (pi), circumference, and area.

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Composite Figures

Figures composed of more than one shape can be be broken down into smaller shapes using the additive property of area.

7.9C - determine the area of composite figures containing combinations of rectangles, squares, parallelograms, trapezoids, triangles, semicircles, and quarter circles

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2023-13: a composite figure was given, students had to solve by breaking it down into two trapezoids

2023-26: a composite figure was given, students had to solve by removing sections

2024-12: a composite figure was given, students had to solve by breaking it down into two triangles, two rectangles, and square or two trapezoids and a square

2024-36: a composite figure was given, students had to solve by breaking it down into a trapezoid and a rectangle or two triangles and a rectangle

2025-12: a composite figure was given, students had to solve by breaking it down into two triangles and a rectangle or a triangle and a rectangle

2025-22: a composite figure was given, students had to solve by breaking it down into two rectangles

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Circle Geometry

First introduced in 7th grade, students begin to explore π (pi) and the circumference and area of circles.

7.5B - describe π as the ratio of the circumference of a circle to its diameter

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2024-33: the radius was given, students had to describe π in terms of the circumference and diameter

2025-14: the radius was given and circumference were given, students had to describe π in terms of the circumference and diameter

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7.9B - determine the circumference and area of circles

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2023-8: the diameter was given, students had to solve for the area

2023-37: the radius was given, students had to solve for the circumference

2024-14: the area was given, students had to solve for the radius

2024-25: the diameter was given, students had to solve for the area

2025-8: the diameter was given, students had to solve for the area and circumference

2025-29: the circumference was given, students had to solve for the diameter