24. Full Mixed Review Strategy

On a mixed GED® geometry set, slow down for the first 5 seconds and classify the problem.

Use this routine:

• Name the shape or situation.
• Decide what is being asked.
• Pick the formula or rule.
• Estimate the size of the answer.
• Check the unit.

Fast clue words:

• Fence, border, trim = perimeter.
• Carpet, paint, tile = area.
• Fill, hold, capacity = volume.
• Wrap, label, cover the outside = surface area.
• Diagonal, ladder, shortest distance = Pythagorean theorem.
• Degrees, lines, triangle = angle rules.

Common mistake: doing correct arithmetic for the wrong measurement.

Deepen your understanding
Use this focused guide to turn Full Mixed Review Strategy into a dependable GED® problem-solving skill.

Learning targets

• Classify mixed geometry questions quickly and select a matching formula or rule.
• Use estimation, units, and diagram markings to eliminate distractors.
• Manage time by separating immediate, multi-step, and return-later questions.

Step-by-step solving routine

1. Read the final sentence first, then annotate the diagram and givens.
2. Name the target quantity and expected unit before opening the formula sheet or calculator.
3. Write one formula line, one substitution line, and one calculation line to reduce input errors.
4. Audit the answer for unit, size, rounding, and whether every condition in the question was used.

GED® application
On a mixed set, a practical first pass answers direct formula and angle-sum questions. A second pass handles composite figures and multi-step applications. Marking a hard question and returning later protects time without turning a temporary obstacle into a guessed answer.

Coach check
Keep an error log with four labels—classification, formula, arithmetic, and unit—so review targets the actual reason for each miss.

Visual study gallery
Study each diagram before the worked examples. Name what is measured, identify the needed dimensions or relationships, and explain which formula or rule the picture supports.

10 worked examples and problem solving
Use these examples as guided practice before attempting the session MCQs. Each problem is self-contained, including any needed table or context.

Example 1
Problem: A room is \(12\) ft by \(10\) ft. How many square feet of carpet are needed?
Answer: \(120\) square feet
Solution: Carpet covers area: \(12 \times 10 = 120\). Pro tip: every table or context needed is included in the question itself.

Example 2
Problem: A yard is \(12\) ft by \(10\) ft. How many feet of fence go around it?
Answer: \(44\) feet
Solution: Fence uses perimeter: \(2\)(\(12+10\))=\(44\). Pro tip: every table or context needed is included in the question itself.

Example 3
Problem: A box is \(5\) by \(4\) by \(3\). How much can it hold?
Answer: \(60\) cubic units
Solution: Hold means volume: \(5 \times 4 \times 3 = 60\). Pro tip: every table or context needed is included in the question itself.

Example 4
Problem: A box is \(5\) by \(4\) by \(3\). How much material covers its outside?
Answer: \(94\) square units
Solution: Covering outside means surface area: \(2\)(\(20+15+12\))=\(94\). Pro tip: every table or context needed is included in the question itself.

Example 5
Problem: A circle has radius \(4\). Using \(\pi\)=\(3.14\), what is its area?
Answer: \(50.24\)
Solution: Area is \(\pi\) \(r^2\): \(3.14 \times 16 = 50.24\). Pro tip: every table or context needed is included in the question itself.

Example 6
Problem: A circle has radius \(4\). Using \(\pi\)=\(3.14\), what is its circumference?
Answer: \(25.12\)
Solution: Circumference is \(2\) \(\pi\) r: \(2 \times 3.14 \times 4 = 25.12\). Pro tip: every table or context needed is included in the question itself.

Example 7
Problem: A rectangle is \(6\) by \(8\). What is its diagonal?
Answer: \(10\)
Solution: The diagonal is the hypotenuse: \(\sqrt{6^2+8^2}=10\). Pro tip: every table or context needed is included in the question itself.

Example 8
Problem: A triangle has angles \(35^\circ\) and \(85^\circ\). What is the third angle?
Answer: \(60^\circ\)
Solution: Triangle angles add to \(180\): \(180-35-85=60\). Pro tip: every table or context needed is included in the question itself.

Example 9
Problem: A table lists a rectangle with length \(9\) and width \(7\). What is its area?

Answer: \(63\) square units
Solution: The table gives all needed dimensions in the question. Area is \(9 \times 7 = 63\). Pro tip: every table or context needed is included in the question itself.

Example 10
Problem: A table lists a cylinder with radius \(3\) and height \(6\). Using \(\pi\)=\(3.14\), what is its volume?

Answer: \(169.56\)
Solution: The table gives radius and height. Cylinder volume is \(3.14 \times 3^2 \times 6 = 169.56\). Pro tip: every table or context needed is included in the question itself.

Additional resources

• Mixed-review checklist: identify the shape, the requested measurement, the formula, and the unit.
• Table-reading drill: copy every number from the question or table before choosing a formula.