Perimeter & Area

41 problem types · Pick a group to see its problem types.

18 Grades 2–4

Perimeter by Tracing Every Side

The perimeter of a composite or overlapped figure is found by following its boundary and summing each side, using rectangle/square side equalities and overlap relations to recover unknown segments. Learners trace joined rectangles, ribbons around boxes, and overlapped polygons, later with fractional and decimal side lengths. The discipline is accounting for every boundary segment exactly once.

Tile and Cut Figures with Congruent Pieces

A region is cut into, or built from, congruent pieces; the piece count, a side length, or the total area follows from how the copies fit. Learners recover a side from the number of cut pieces, count grid cards, identify tiling pieces and area, and read a base shape from solid views. It links multiplication and division to spatial structure.

10 Grades 5–7

Area by Decomposition

Find a region’s area by cutting it into rectangles and triangles (or relating shared and overlapping sub-regions) and adding or subtracting their areas; choose the base–height pair that makes each piece computable.

Circumference and Area of a Circle

Length and area for a shape with no straight sides. A part of a circle is measured by its share of the whole turn, so a central angle out of 360 does for a circle what a fraction does for a bar. Mixed boundaries -- some straight, some curved -- are handled piece by piece, and rolling turns circumference into distance.

Perimeter by Tracing Every Side ↑ All groups

Composite perimeter sums boundary edges Measurement & data

Find perimeter path length by multiplication Measurement & dataOperations

Perimeter as side length times side count Measurement & dataOperations

Ribbon around a box: four equal parts Measurement & data

Distance between parallel sides equals the side length GeometryMeasurement & data

Find a missing side, then sum sides as fractions FractionsMeasurement & data

Find a side from equal perimeters Measurement & dataOperations

Overlapping rectangles' edges form the outline Measurement & data

Perimeter as a multiple of a unit length Measurement & data

Perimeter by tracing every side Measurement & data

Perimeter of overlapped squares and rectangles Measurement & dataGeometry

Perimeter plus tiles needed to build it Measurement & dataOperations

Side lengths from overlapping rectangles Measurement & dataOperations

Slide edges to rectangle; perimeter unchanged Measurement & data

Perimeter as decimal side sums minus overlaps Base-ten numbersMeasurement & data

Perimeter is the sum of all side lengths FractionsMeasurement & data

Find cube edge from net perimeter GeometryMeasurement & data

Complete point-symmetric figure to find perimeter GeometryMeasurement & data

Tile and Cut Figures with Congruent Pieces ↑ All groups

Cut a rectangle into a grid of cards GeometryMeasurement & data

Recover side length from number of cut pieces OperationsMeasurement & data

Base perimeter from multiple views Measurement & dataGeometry

Count distinct shapes built by adding congruent tiles Geometry

Identify tiling pieces and total area GeometryMeasurement & data

Area by Decomposition ↑ All groups

Equal overlap area yields a segment length Measurement & data

Decompose composite figures into rectangles Base-ten numbersMeasurement & data

Count how many unit shapes make the whole GeometryFractions

One ■-th of the whole is the whole divided by ■ GeometryNumber system

Solve known areas first, step by step GeometryMeasurement & data

Triangle height depends on chosen base Geometry

Use shared base to find composite area GeometryMeasurement & data

Box the triangle, subtract the corner triangles GeometryNumber system

Slide pieces so the shaded part becomes one lump Geometry

Trapezoid minus two right triangles, in letters GeometryExpressions

Circumference and Area of a Circle ↑ All groups

A circle's snug square has the diameter as its side Geometry

A part's share of a circle is its central angle's share GeometryRatios

Draw a line to split it into straight and curved pieces Geometry

For equal thickness the material ratio is the area ratio GeometryRatios

Match the traced circle's circumference to the cone Geometry

Measure straight parts as sides, curved parts as arcs Geometry

One full roll moves it its own circumference Geometry

Angles adding past 360° cover more than one circle Geometry