Measurement, Area, and Volume flashcards

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Trapezoid measurementPerimeter and Area of Plane Figures: Average the parallel bases, then multiply by the height.
When should I use perimeter?Perimeter and Area of Plane Figures: Add all outer side lengths.
What method supports trapezoid measurement?Perimeter and Area of Plane Figures: A=(b₁+b₂)h/2
Area of triangles and parallelogramsPerimeter and Area of Plane Figures: Use the straight-up height, not the slanted edge.
PerimeterPerimeter and Area of Plane Figures: Walk around the outside and add the lengths.
What must I check in perimeter and area of plane figures?Perimeter and Area of Plane Figures: Perimeter uses linear units; area uses square units; a triangle height must be perpendicular to its base
What method supports area of triangles and parallelograms?Perimeter and Area of Plane Figures: triangle A=bh/2; parallelogram A=bh; trapezoid A=(b₁+b₂)h/2
What method supports perimeter?Perimeter and Area of Plane Figures: rectangle perimeter=2(l+w)
When should I use trapezoid measurement?Perimeter and Area of Plane Figures: Use the mean of parallel bases in an area calculation.
When should I use area of triangles and parallelograms?Perimeter and Area of Plane Figures: Use a perpendicular height with the correct shape factor.
Missing dimensions from areaComposite Figures and Missing Dimensions: Turn the total area into an equation for the missing side.
When should I use subtract a missing region?Composite Figures and Missing Dimensions: Find composite area by subtracting a hole from a whole.
What method supports missing dimensions from area?Composite Figures and Missing Dimensions: rectangle width=(total area−known component area)/length
Partition a composite shapeComposite Figures and Missing Dimensions: Break the shape into familiar pieces without double-counting.
Subtract a missing regionComposite Figures and Missing Dimensions: Big area minus the cutout gives what remains.
What must I check in composite figures and missing dimensions?Composite Figures and Missing Dimensions: Subtract only regions that lie inside the stated whole; do not assume a figure is drawn to scale
What method supports partition a composite shape?Composite Figures and Missing Dimensions: total area=sum of nonoverlapping part areas
What method supports subtract a missing region?Composite Figures and Missing Dimensions: remaining area=outer area−cutout area
When should I use missing dimensions from area?Composite Figures and Missing Dimensions: Use a composite-area equation to recover a length.
When should I use partition a composite shape?Composite Figures and Missing Dimensions: Add nonoverlapping pieces to find a total.
Exposed faces of joined solidsSurface Area of Solids: Remove both copies of the face that becomes hidden.
When should I use rectangular solid surface area?Surface Area of Solids: Add the six face areas of a closed box.
What method supports exposed faces of joined solids?Surface Area of Solids: joined exposed area=SA₁+SA₂−2·shared area
Curved-solid surface areaSurface Area of Solids: Identify which surfaces are exposed and which height the formula uses.
Rectangular solid surface areaSurface Area of Solids: Count both faces for each dimension pair.
What must I check in surface area of solids?Surface Area of Solids: Surface area is an editorial supporting extension; include only exposed faces and state whether ends or tops are present
What method supports curved-solid surface area?Surface Area of Solids: cylinder SA=2πrh+2πr²; closed cone SA=πrℓ+πr²; sphere SA=4πr²
What method supports rectangular solid surface area?Surface Area of Solids: SA=2(lw+lh+wh)
When should I use exposed faces of joined solids?Surface Area of Solids: Subtract hidden shared faces from a sum of surface areas.
When should I use curved-solid surface area?Surface Area of Solids: Distinguish curved surfaces from circular bases.
Spheres and inverse volumeVolumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: A sphere volume depends on the cube of its radius.
When should I use prisms and cylinders?Volumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: Multiply base area by perpendicular height.
What method supports spheres and inverse volume?Volumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: V_sphere=4πr³/3
Pyramids and conesVolumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: Pointed solids use one third of the matching base-height prism or cylinder.
Prisms and cylindersVolumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: Uniform stacks have base area times height.
What must I check in volumes of prisms, cylinders, pyramids, cones, and spheres?Volumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: Heights in volume formulas are perpendicular; radius is half a supplied diameter; use cubic units
What method supports pyramids and cones?Volumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: V_pyramid=Bh/3; V_cone=πr²h/3
What method supports prisms and cylinders?Volumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: V_prism=Bh; V_cylinder=πr²h
When should I use spheres and inverse volume?Volumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: Use the sphere formula and solve a dimension constraint.
When should I use pyramids and cones?Volumes of Prisms, Cylinders, Pyramids, Cones, and Spheres: Apply one third of base area times height.
Volume and reverse scalingScale Factors for Length, Area, and Volume: A volume ratio must be cube-rooted before it becomes a length ratio.
When should I use length scaling?Scale Factors for Length, Area, and Volume: Apply a similarity factor to a perimeter.
What method supports volume and reverse scaling?Scale Factors for Length, Area, and Volume: V₂/V₁=k³ ⇒ k=∛(V₂/V₁)
Area scalingScale Factors for Length, Area, and Volume: Two scaled dimensions mean two copies of the factor.
Length scalingScale Factors for Length, Area, and Volume: Perimeter is a sum of lengths, so it gets one scale factor.
What must I check in scale factors for length, area, and volume?Scale Factors for Length, Area, and Volume: Length, area, and volume use scale-factor powers 1, 2, and 3 respectively
What method supports area scaling?Scale Factors for Length, Area, and Volume: A₂=k²A₁
What method supports length scaling?Scale Factors for Length, Area, and Volume: P₂=kP₁
When should I use volume and reverse scaling?Scale Factors for Length, Area, and Volume: Take a cube root of a volume ratio to recover a length ratio.
When should I use area scaling?Scale Factors for Length, Area, and Volume: Square the linear scale factor.
Geometry with a cost constraintGeometry Modeling and Multistep Measurement Problems: Undo price first, then undo the geometry formula.
When should I use material needed for a region?Geometry Modeling and Multistep Measurement Problems: Combine area with a per-area coverage rate.
What method supports geometry with a cost constraint?Geometry Modeling and Multistep Measurement Problems: cost=unit cost×area; width=area/length
Volume differenceGeometry Modeling and Multistep Measurement Problems: A new layer has the same base and only the added height.
Material needed for a regionGeometry Modeling and Multistep Measurement Problems: Find area, apply the rate, and count full packages if needed.
What must I check in geometry modeling and multistep measurement problems?Geometry Modeling and Multistep Measurement Problems: Keep unit dimensions consistent and apply any count, packing, or feasibility restrictions after modeling
What method supports volume difference?Geometry Modeling and Multistep Measurement Problems: ΔV=B·Δh for a constant-base prism
What method supports material needed for a region?Geometry Modeling and Multistep Measurement Problems: material=area×rate×coats
When should I use geometry with a cost constraint?Geometry Modeling and Multistep Measurement Problems: Solve for a dimension using an area or volume constraint.
When should I use volume difference?Geometry Modeling and Multistep Measurement Problems: Model an added layer as a difference of volumes.