Determine Missing Side Lengths of a Rectilinear Figure
Determine Missing Side Lengths of a Rectilinear Figure is a Grade 3 math skill from Eureka Math using the geometric property that opposite parallel sides of a rectilinear figure must account for the same total length. If a side of total length c is parallel to two segments of lengths a and b, then c = a + b. To find a missing segment: a = c - b. Third graders apply this reasoning to find unlabeled dimensions on L-shaped and stepped figures before computing perimeter or area, making it a critical prerequisite skill for composite figure problems.
Key Concepts
In a rectilinear figure, the total length of a side is equal to the sum of the lengths of all parallel segments. If a side of total length $c$ is parallel to segments of lengths $a$ and $b$, their relationship is: $$c = a + b$$ To find a missing segment, you can rearrange the formula: $$a = c b$$.
Common Questions
What is a rectilinear figure?
A rectilinear figure is a polygon made entirely of right angles—all sides are either horizontal or vertical. L-shapes, T-shapes, and stepped figures are common examples.
How do you find a missing side length in a rectilinear figure?
The total length of a side equals the sum of all parallel segments on the opposite side: c = a + b. To find a missing segment: missing = total - known. For example, if c = 10 and a = 6, then b = 10 - 6 = 4.
Why does c = a + b hold for parallel sides in a rectilinear figure?
Because horizontal and vertical sides span the same distance when viewed from opposite sides. The total span on one side equals the combined spans of all segments on the opposite side at the same level.
Give an example of finding a missing side in a step-shaped figure.
An L-shape has total height 8 units on the left side. The right portion shows two segments: one of 5 units and one unknown. Missing = 8 - 5 = 3 units.
In which textbook is Determine Missing Side Lengths of a Rectilinear Figure taught?
This skill is taught in Eureka Math, Grade 3.