Rectilinear Figure — Definition, Formula & Examples
A rectilinear figure is a flat shape made entirely of straight sides that meet at right angles (90°). Every corner of the shape is either an inside or outside right angle, giving it a staircase-like appearance.
A rectilinear figure is a polygon in which every interior angle measures either 90° or 270°, meaning all sides are aligned with two perpendicular directions. Such figures are also called orthogonal polygons or rectilinear polygons.
How It Works
To find the area of a rectilinear figure, you can break it into non-overlapping rectangles. Calculate the area of each rectangle, then add the areas together. This decomposition strategy is the key idea behind CCSS standard 3.MD.7d, which asks students to find the area of shapes that can be split into rectangles. You can also find the area by enclosing the figure in one large rectangle and subtracting the missing corner pieces.
Worked Example
Problem: An L-shaped rectilinear figure has an overall width of 6 cm, an overall height of 5 cm, and a 3 cm × 2 cm rectangular piece removed from the upper-right corner. Find its area.
Step 1: Find the area of the full enclosing rectangle.
Step 2: Find the area of the missing rectangular piece.
Step 3: Subtract the missing piece from the full rectangle.
Answer: The area of the L-shaped rectilinear figure is 24 cm².
Why It Matters
CCSS 3.MD.7d specifically asks students to find the area of rectilinear figures by decomposing them into rectangles. Understanding this term helps teachers and students connect the standard's language to the hands-on strategy of splitting complex shapes into simpler ones.
Common Mistakes
Mistake: Thinking any polygon with straight sides is rectilinear.
Correction: A rectilinear figure must have all right angles. A triangle or a regular hexagon has straight sides but is not rectilinear because its angles are not all 90° or 270°.