Area and perimeter builder

What the builder shows

Area is how many unit squares cover a shape. Perimeter is the distance around the outside, counted in unit edges. On this page, tap a square to color it and tap again to clear it, or drag across the grid to color or rub out several at once. The red line follows the outside edge, and the readout gives both totals. When the shape is a rectangle, the readout shows the multiplication for the area and the addition for the perimeter.

Three modes are available. Free build is open play. Same area, different perimeter gives an area and keeps a list of every perimeter the child finds for it. Hit the target asks for one shape with a given area and perimeter, with the numbers hidden so the child counts. Number the squares writes a count in each square.

Why build it by hand

Children often learn area and perimeter as two formulas and then mix them up. Building with squares keeps the meaning in view: adding a square always adds 1 to the area, but it can add 2 to the perimeter, add nothing, or even take 2 away, depending on how many edges it shares. Common Core standard 3.MD.D.8 asks students to show rectangles with the same area and different perimeters, and this is exactly what the second mode practices.

Common mix-ups

• Thinking more area always means more perimeter. A 1 by 12 strip and a 4 by 4 square show it is not true: area 12 with perimeter 26, and area 16 with perimeter 16.
• Counting corner squares twice for perimeter. Count edges, not squares; a corner square adds two edges.
• Forgetting inside edges around a hole. The edge of a hole is part of the boundary, so it counts toward the perimeter.
• Writing the wrong units. Area is in square units and perimeter is in units.

A 10-minute lesson

• Build a 2 by 6 rectangle. Ask for the area and the perimeter, then check.
• Switch to Same area, different perimeter and let the child build two or three shapes for the target area.
• Ask: which shape had the shortest perimeter? It is usually the most square-like one.
• Try Hit the target with the numbers hidden. The child counts squares and edges to check before the cheer appears.
• End by asking the child to explain the difference between area and perimeter in one sentence.

Where it fits by grade

• Grade 3: area by counting unit squares (3.MD.C.6), area and multiplication (3.MD.C.7), and perimeter problems (3.MD.D.8).
• Grade 4: area and perimeter formulas for rectangles (4.MD.A.3).
• England: Year 4 finds perimeter and area of rectilinear shapes by counting, Year 5 compares areas of rectangles, and Year 6 recognizes that shapes with the same area can have different perimeters and vice versa.

Learning more

Area and perimeter are on Eurekami's skill map, so Daily Practice can bring them back when they start to fade. Lessons draw diagrams live from the numbers in each question, and teachers can print worksheets with answer keys on the same skill.