8.1 Area, Volume, and Composite Figures
Key Takeaways
- GED Math geometry questions usually test choosing the correct measurement idea before substituting numbers into a formula.
- Perimeter and circumference use ordinary linear units, area uses square units, and volume uses cubic units.
- Composite 2-D figures should be split into familiar rectangles, triangles, circles, or trapezoids before adding or subtracting areas.
- Composite 3-D figures require the same logic as 2-D figures: find each solid's volume or surface area, then combine only the parts requested.
- The GED formula sheet helps with formulas, but candidates still must identify radius versus diameter, height versus slant height, and area versus surface area.
Start With What Is Being Measured
The GED Mathematical Reasoning test includes quantitative problem solving in measurement, so geometry is usually presented as a practical task: tile a floor, fence a yard, fill a tank, paint a box, or compare package sizes. The first decision is not which numbers to multiply. The first decision is what kind of measurement the question asks for.
Use the unit as a warning signal. Perimeter and circumference measure distance around an object, so the answer uses feet, inches, meters, or another ordinary unit. Area measures flat coverage and uses square units. Volume measures capacity or inside space and uses cubic units. Surface area measures outside covering on a solid, so it also uses square units even though the object is 3-D.
GED Geometry Decision Table
| Prompt language | Likely measure | Unit check |
|---|---|---|
| Fence, trim, border, distance around | Perimeter or circumference | Linear units |
| Carpet, paint on one wall, land, shaded region | Area | Square units |
| Water, storage, air, soil, concrete inside | Volume | Cubic units |
| Wrapping, outside paint on a box, label on a can | Surface area | Square units |
| Missing side in a right triangle | Pythagorean theorem | Linear units |
Composite Figures
A composite figure is made from smaller familiar figures. On GED Math, a composite shape may be an L-shaped room, a rectangle with a semicircle attached, a shaded region with a cutout, or a solid made from two prisms. The safest approach is to draw a mental boundary, label the simple parts, calculate each part, then decide whether the problem asks for a total or a leftover.
For a 2-D example, suppose a playground is a 30 ft by 18 ft rectangle with a 10 ft by 6 ft sandbox removed. The full rectangle area is 30 * 18 = 540 square feet. The sandbox area is 10 * 6 = 60 square feet. The remaining play area is 540 - 60 = 480 square feet. The word removed tells you to subtract, not add.
For a 3-D example, suppose a storage container is made of a rectangular prism 8 ft long, 4 ft wide, and 3 ft high, plus a second prism on top that is 4 ft long, 4 ft wide, and 2 ft high. The bottom volume is 8 * 4 * 3 = 96 cubic feet. The top volume is 4 * 4 * 2 = 32 cubic feet. The total capacity is 128 cubic feet if the two solids are connected inside.
Formula-Sheet Traps
The GED provides a formula sheet, but the sheet does not choose the formula for you. A circle formula uses radius, so if the question gives diameter, divide by 2 before using r. A cylinder volume problem needs base area times height, not circumference times height. A surface area problem may require only the exposed faces, not every face in the formula, if one side is against a wall or another solid.
Worked Mini-Example
A circular garden has diameter 12 ft and is surrounded by a rectangular walkway that is 18 ft by 16 ft. How much walkway area is outside the garden? The rectangle area is 18 * 16 = 288 square feet. The garden radius is 12 / 2 = 6 ft, so the circle area is about 3.14 * 6^2 = 113.04 square feet. The walkway area is 288 - 113.04 = 174.96 square feet.
Before choosing an answer, label the result. If the prompt asks for area and your answer is in feet instead of square feet, your process is off. If a volume answer is smaller than the matching floor area even though height is greater than 1, check whether you forgot the height. This reasonableness check is fast and GED-specific because many answer choices are built from common formula or unit mistakes.
A rectangular kitchen floor is 16 feet long and 11 feet wide. A rectangular island that is 5 feet by 3 feet will not be tiled. How many square feet of tile are needed for the exposed floor?
A cylinder has radius 4 inches and height 9 inches. Which expression gives its volume?