How can I check an unknown side length in a composite shape?
Quick answer
First identify which smaller segments lie along the same straight side and together make the marked whole. Subtract the known segment lengths from that whole to find the missing length. Then add the known and missing parts back together; they should equal the whole. For example, if a side is 10 units long and one aligned part is 4, the other part is 6 units. [S1]
The question, the details, the next step.
I have a composite shape with one side split into two parts, but one part has no label. How do I know what to subtract?
Start by finding the whole side: look for a length label that applies to the complete straight edge, or use the outline to see which smaller segments continue along that edge. Then check that the labeled smaller segment and the unknown segment together span that whole. Lengths on different edges do not combine just because they are near each other in the drawing.
Once you have established that the pieces make up the whole, use:
unknown part = whole length − known part
For instance, if a whole side is marked 10 units and one aligned part is 4 units, the missing part is 10 − 4 = 6 units. OpenStax uses this kind of aligned-length subtraction in its geometry examples. [S1]
The shape is stepped, like an L. How can I tell whether two short edges belong to the same total?
Trace the boundary with your finger or pencil. Segments belong to the same total when they lie end-to-end on one straight line and together cover the full edge whose length is labeled. In a stepped outline, two horizontal segments may add up to a longer horizontal span, for example, but a vertical segment cannot be part of that horizontal total.
Use the labels and the connections between edges to establish which parts make up the whole. If the diagram does not show or state that relationship clearly, the missing length may not be determined from the information given.
Can you show the subtraction and the check with a simple example?
Assume a diagram marks one complete straight side as 13 cm. It is divided into two aligned pieces: one is labeled 8 cm and the other is unknown.
- Subtract the known piece: 13 − 8 = 5 cm.
- Add the pieces back: 8 + 5 = 13 cm.
The check works because the parts must total the stated whole. If your addition gives a different number, revisit the labels, the units, and whether you matched the correct segments. The subtraction method is the same as the whole-and-part examples in the cited geometry material; the 13 cm example here is illustrative. [S1]
What if the diagram gives several lengths, or I get zero or a negative answer?
Write down only the lengths that lie along the same whole edge. If that edge is split into more than two parts, subtract all the known parts from the whole: unknown = whole − (known part 1 + known part 2 + …). Then add every part, including your answer, to check that their total matches the whole.
A zero or negative result is a reason to check your setup. You may have used a length from another edge, added a whole and one of its parts together, or copied a label incorrectly. If the labels and alignment are clear but the numbers still conflict, the diagram may contain inconsistent information. Use the stated lengths and relationships to check it.
A practical checklist
Find the labeled whole edge you are trying to split.
Trace the edge and confirm which smaller segments lie end-to-end along it.
Check that the whole and parts use the same units.
Subtract the sum of known parts from the whole.
Add all parts back together and compare the sum with the stated whole.
A few more useful answers
Can I use the apparent size of the segments in the drawing?
Use the labels and the edge relationships, not visual measurement. Apparent lengths are not a substitute for stated information.
What if I cannot tell which segments make up the whole?
Do not guess from proximity alone. Trace the straight edge and look for labels or markings that establish the relationship; if it remains unclear, ask for a clearer diagram or more information.
How do I check a side split into three or more parts?
Add the known parts, subtract their sum from the whole to find the missing part, then add every part together to verify the total.
Sources
References used for this guide.
- [S1] OpenStax Prealgebra 2e: Solve Geometry Applications—Circles and Irregular Figures openstax.org · Checked