2D Shapes Area and Perimeter Table & Solver
Perimeter is the distance around a shape and area is the space inside it. This directory lists the formulas for six common 2D shapes, a live shape solver with diagram, and 120 searchable worked examples.
SquareP = 4sA = s²
RectangleP = 2(l + w)A = l × w
ParallelogramP = 2(a + b)A = b × h
TrapezoidP = a + b + c + dA = ½(a + b)h
RhombusP = 4sA = ½ d1 d2
Regular HexagonP = 6sA = (3√3 / 2) s²
Shape Selector & Live Diagram
Tip: open this page with ?shape=trapezoid (square, rectangle, parallelogram, trapezoid, rhombus or hexagon) to start with that shape and its row highlighted.
| Shape Name | Required Dimensions | Perimeter Formula | Area Formula | Copy Row |
|---|---|---|---|---|
| Square | Side (s) | P = 4s | A = s² | |
| Rectangle | Length (l), Width (w) | P = 2(l + w) | A = l × w | |
| Parallelogram | Base (b), Side (a), Height (h) | P = 2(a + b) | A = b × h | |
| Trapezoid | Bases (a, b), Legs (c, d), Height (h) | P = a + b + c + d | A = ½ × (a + b) × h | |
| Rhombus | Diagonals (d1, d2) | P = 4s, where s = √(d1² + d2²) / 2 | A = ½ × d1 × d2 | |
| Regular Hexagon | Side (s) | P = 6s | A = (3√3 / 2) × s² |
| Shape | Dimensions | Perimeter (P) | Area (A) | Copy |
|---|---|---|---|---|
| Square | s = 5 | 20 | 25 | |
| Rectangle | l = 8, w = 5 | 26 | 40 | |
| Parallelogram | b = 10, a = 6, h = 4 | 32 | 40 | |
| Trapezoid | a = 12, b = 6, c = 5, d = 5, h = 4 | 28 | 36 | |
| Rhombus | d1 = 10, d2 = 6 | 23.3238 | 30 | |
| Regular Hexagon | s = 6 | 36 | 93.5307 |
120 Searchable Worked Examples
| Shape | Dimensions | Perimeter (P) | Area (A) | Worked Solution | Copy |
|---|---|---|---|---|---|
| Square | s = 1 | 4 | 1 | P = 4 × 1 = 4; A = 1² = 1 | |
| Square | s = 2 | 8 | 4 | P = 4 × 2 = 8; A = 2² = 4 | |
| Square | s = 3 | 12 | 9 | P = 4 × 3 = 12; A = 3² = 9 | |
| Square | s = 4 | 16 | 16 | P = 4 × 4 = 16; A = 4² = 16 | |
| Square | s = 5 | 20 | 25 | P = 4 × 5 = 20; A = 5² = 25 | |
| Square | s = 6 | 24 | 36 | P = 4 × 6 = 24; A = 6² = 36 | |
| Square | s = 7 | 28 | 49 | P = 4 × 7 = 28; A = 7² = 49 | |
| Square | s = 8 | 32 | 64 | P = 4 × 8 = 32; A = 8² = 64 | |
| Square | s = 9 | 36 | 81 | P = 4 × 9 = 36; A = 9² = 81 | |
| Square | s = 10 | 40 | 100 | P = 4 × 10 = 40; A = 10² = 100 | |
| Square | s = 12 | 48 | 144 | P = 4 × 12 = 48; A = 12² = 144 | |
| Square | s = 15 | 60 | 225 | P = 4 × 15 = 60; A = 15² = 225 | |
| Square | s = 20 | 80 | 400 | P = 4 × 20 = 80; A = 20² = 400 | |
| Square | s = 25 | 100 | 625 | P = 4 × 25 = 100; A = 25² = 625 | |
| Square | s = 30 | 120 | 900 | P = 4 × 30 = 120; A = 30² = 900 | |
| Square | s = 50 | 200 | 2500 | P = 4 × 50 = 200; A = 50² = 2500 | |
| Square | s = 100 | 400 | 10000 | P = 4 × 100 = 400; A = 100² = 10000 | |
| Square | s = 0.5 | 2 | 0.25 | P = 4 × 0.5 = 2; A = 0.5² = 0.25 | |
| Square | s = 2.5 | 10 | 6.25 | P = 4 × 2.5 = 10; A = 2.5² = 6.25 | |
| Square | s = 7.5 | 30 | 56.25 | P = 4 × 7.5 = 30; A = 7.5² = 56.25 | |
| Rectangle | l = 2, w = 1 | 6 | 2 | P = 2(2 + 1) = 6; A = 2 × 1 = 2 | |
| Rectangle | l = 3, w = 2 | 10 | 6 | P = 2(3 + 2) = 10; A = 3 × 2 = 6 | |
| Rectangle | l = 4, w = 3 | 14 | 12 | P = 2(4 + 3) = 14; A = 4 × 3 = 12 | |
| Rectangle | l = 5, w = 4 | 18 | 20 | P = 2(5 + 4) = 18; A = 5 × 4 = 20 | |
| Rectangle | l = 6, w = 4 | 20 | 24 | P = 2(6 + 4) = 20; A = 6 × 4 = 24 | |
| Rectangle | l = 7, w = 5 | 24 | 35 | P = 2(7 + 5) = 24; A = 7 × 5 = 35 | |
| Rectangle | l = 8, w = 5 | 26 | 40 | P = 2(8 + 5) = 26; A = 8 × 5 = 40 | |
| Rectangle | l = 9, w = 6 | 30 | 54 | P = 2(9 + 6) = 30; A = 9 × 6 = 54 | |
| Rectangle | l = 10, w = 4 | 28 | 40 | P = 2(10 + 4) = 28; A = 10 × 4 = 40 | |
| Rectangle | l = 10, w = 6 | 32 | 60 | P = 2(10 + 6) = 32; A = 10 × 6 = 60 | |
| Rectangle | l = 12, w = 8 | 40 | 96 | P = 2(12 + 8) = 40; A = 12 × 8 = 96 | |
| Rectangle | l = 15, w = 10 | 50 | 150 | P = 2(15 + 10) = 50; A = 15 × 10 = 150 | |
| Rectangle | l = 16, w = 9 | 50 | 144 | P = 2(16 + 9) = 50; A = 16 × 9 = 144 | |
| Rectangle | l = 20, w = 12 | 64 | 240 | P = 2(20 + 12) = 64; A = 20 × 12 = 240 | |
| Rectangle | l = 25, w = 10 | 70 | 250 | P = 2(25 + 10) = 70; A = 25 × 10 = 250 | |
| Rectangle | l = 30, w = 20 | 100 | 600 | P = 2(30 + 20) = 100; A = 30 × 20 = 600 | |
| Rectangle | l = 40, w = 25 | 130 | 1000 | P = 2(40 + 25) = 130; A = 40 × 25 = 1000 | |
| Rectangle | l = 50, w = 30 | 160 | 1500 | P = 2(50 + 30) = 160; A = 50 × 30 = 1500 | |
| Rectangle | l = 8.5, w = 4 | 25 | 34 | P = 2(8.5 + 4) = 25; A = 8.5 × 4 = 34 | |
| Rectangle | l = 12.5, w = 6 | 37 | 75 | P = 2(12.5 + 6) = 37; A = 12.5 × 6 = 75 | |
| Parallelogram | b = 5, a = 4, h = 3 | 18 | 15 | P = 2(4 + 5) = 18; A = 5 × 3 = 15 | |
| Parallelogram | b = 6, a = 5, h = 4 | 22 | 24 | P = 2(5 + 6) = 22; A = 6 × 4 = 24 | |
| Parallelogram | b = 8, a = 5, h = 4 | 26 | 32 | P = 2(5 + 8) = 26; A = 8 × 4 = 32 | |
| Parallelogram | b = 10, a = 6, h = 4 | 32 | 40 | P = 2(6 + 10) = 32; A = 10 × 4 = 40 | |
| Parallelogram | b = 10, a = 7, h = 5 | 34 | 50 | P = 2(7 + 10) = 34; A = 10 × 5 = 50 | |
| Parallelogram | b = 12, a = 8, h = 6 | 40 | 72 | P = 2(8 + 12) = 40; A = 12 × 6 = 72 | |
| Parallelogram | b = 9, a = 5, h = 3 | 28 | 27 | P = 2(5 + 9) = 28; A = 9 × 3 = 27 | |
| Parallelogram | b = 14, a = 10, h = 8 | 48 | 112 | P = 2(10 + 14) = 48; A = 14 × 8 = 112 | |
| Parallelogram | b = 15, a = 13, h = 12 | 56 | 180 | P = 2(13 + 15) = 56; A = 15 × 12 = 180 | |
| Parallelogram | b = 20, a = 10, h = 8 | 60 | 160 | P = 2(10 + 20) = 60; A = 20 × 8 = 160 | |
| Parallelogram | b = 7, a = 5, h = 4 | 24 | 28 | P = 2(5 + 7) = 24; A = 7 × 4 = 28 | |
| Parallelogram | b = 11, a = 9, h = 6 | 40 | 66 | P = 2(9 + 11) = 40; A = 11 × 6 = 66 | |
| Parallelogram | b = 16, a = 12, h = 9 | 56 | 144 | P = 2(12 + 16) = 56; A = 16 × 9 = 144 | |
| Parallelogram | b = 18, a = 13, h = 5 | 62 | 90 | P = 2(13 + 18) = 62; A = 18 × 5 = 90 | |
| Parallelogram | b = 25, a = 17, h = 15 | 84 | 375 | P = 2(17 + 25) = 84; A = 25 × 15 = 375 | |
| Parallelogram | b = 30, a = 20, h = 16 | 100 | 480 | P = 2(20 + 30) = 100; A = 30 × 16 = 480 | |
| Parallelogram | b = 12, a = 10, h = 8 | 44 | 96 | P = 2(10 + 12) = 44; A = 12 × 8 = 96 | |
| Parallelogram | b = 6.5, a = 5, h = 4 | 23 | 26 | P = 2(5 + 6.5) = 23; A = 6.5 × 4 = 26 | |
| Parallelogram | b = 9, a = 7.5, h = 6 | 33 | 54 | P = 2(7.5 + 9) = 33; A = 9 × 6 = 54 | |
| Parallelogram | b = 24, a = 25, h = 7 | 98 | 168 | P = 2(25 + 24) = 98; A = 24 × 7 = 168 | |
| Trapezoid | a = 12, b = 6, c = 5, d = 5, h = 4 | 28 | 36 | P = 12 + 6 + 5 + 5 = 28; A = ½ × (12 + 6) × 4 = 36 | |
| Trapezoid | a = 10, b = 4, c = 5, d = 5, h = 4 | 24 | 28 | P = 10 + 4 + 5 + 5 = 24; A = ½ × (10 + 4) × 4 = 28 | |
| Trapezoid | a = 14, b = 8, c = 5, d = 5, h = 4 | 32 | 44 | P = 14 + 8 + 5 + 5 = 32; A = ½ × (14 + 8) × 4 = 44 | |
| Trapezoid | a = 16, b = 10, c = 5, d = 5, h = 4 | 36 | 52 | P = 16 + 10 + 5 + 5 = 36; A = ½ × (16 + 10) × 4 = 52 | |
| Trapezoid | a = 15, b = 5, c = 13, d = 13, h = 12 | 46 | 120 | P = 15 + 5 + 13 + 13 = 46; A = ½ × (15 + 5) × 12 = 120 | |
| Trapezoid | a = 17, b = 7, c = 13, d = 13, h = 12 | 50 | 144 | P = 17 + 7 + 13 + 13 = 50; A = ½ × (17 + 7) × 12 = 144 | |
| Trapezoid | a = 20, b = 10, c = 13, d = 13, h = 12 | 56 | 180 | P = 20 + 10 + 13 + 13 = 56; A = ½ × (20 + 10) × 12 = 180 | |
| Trapezoid | a = 14, b = 6, c = 5, d = 5, h = 3 | 30 | 30 | P = 14 + 6 + 5 + 5 = 30; A = ½ × (14 + 6) × 3 = 30 | |
| Trapezoid | a = 20, b = 8, c = 10, d = 10, h = 8 | 48 | 112 | P = 20 + 8 + 10 + 10 = 48; A = ½ × (20 + 8) × 8 = 112 | |
| Trapezoid | a = 22, b = 10, c = 10, d = 10, h = 8 | 52 | 128 | P = 22 + 10 + 10 + 10 = 52; A = ½ × (22 + 10) × 8 = 128 | |
| Trapezoid | a = 28, b = 12, c = 17, d = 17, h = 15 | 74 | 300 | P = 28 + 12 + 17 + 17 = 74; A = ½ × (28 + 12) × 15 = 300 | |
| Trapezoid | a = 27, b = 9, c = 15, d = 15, h = 12 | 66 | 216 | P = 27 + 9 + 15 + 15 = 66; A = ½ × (27 + 9) × 12 = 216 | |
| Trapezoid | a = 29, b = 15, c = 25, d = 25, h = 24 | 94 | 528 | P = 29 + 15 + 25 + 25 = 94; A = ½ × (29 + 15) × 24 = 528 | |
| Trapezoid | a = 34, b = 10, c = 20, d = 20, h = 16 | 84 | 352 | P = 34 + 10 + 20 + 20 = 84; A = ½ × (34 + 10) × 16 = 352 | |
| Trapezoid | a = 34, b = 14, c = 26, d = 26, h = 24 | 100 | 576 | P = 34 + 14 + 26 + 26 = 100; A = ½ × (34 + 14) × 24 = 576 | |
| Trapezoid | a = 22, b = 6, c = 10, d = 10, h = 6 | 48 | 84 | P = 22 + 6 + 10 + 10 = 48; A = ½ × (22 + 6) × 6 = 84 | |
| Trapezoid | a = 8, b = 5, c = 4, d = 5, h = 4 | 22 | 26 | P = 8 + 5 + 4 + 5 = 22; A = ½ × (8 + 5) × 4 = 26 | |
| Trapezoid | a = 14, b = 9, c = 12, d = 13, h = 12 | 48 | 138 | P = 14 + 9 + 12 + 13 = 48; A = ½ × (14 + 9) × 12 = 138 | |
| Trapezoid | a = 18, b = 12, c = 8, d = 10, h = 8 | 48 | 120 | P = 18 + 12 + 8 + 10 = 48; A = ½ × (18 + 12) × 8 = 120 | |
| Trapezoid | a = 15, b = 7, c = 15, d = 17, h = 15 | 54 | 165 | P = 15 + 7 + 15 + 17 = 54; A = ½ × (15 + 7) × 15 = 165 | |
| Rhombus | d1 = 6, d2 = 8 | 20 | 24 | s = √(6² + 8²) / 2 = √100 / 2 = 5; P = 4 × 5 = 20; A = ½ × 6 × 8 = 24 | |
| Rhombus | d1 = 10, d2 = 24 | 52 | 120 | s = √(10² + 24²) / 2 = √676 / 2 = 13; P = 4 × 13 = 52; A = ½ × 10 × 24 = 120 | |
| Rhombus | d1 = 16, d2 = 30 | 68 | 240 | s = √(16² + 30²) / 2 = √1156 / 2 = 17; P = 4 × 17 = 68; A = ½ × 16 × 30 = 240 | |
| Rhombus | d1 = 12, d2 = 16 | 40 | 96 | s = √(12² + 16²) / 2 = √400 / 2 = 10; P = 4 × 10 = 40; A = ½ × 12 × 16 = 96 | |
| Rhombus | d1 = 18, d2 = 24 | 60 | 216 | s = √(18² + 24²) / 2 = √900 / 2 = 15; P = 4 × 15 = 60; A = ½ × 18 × 24 = 216 | |
| Rhombus | d1 = 30, d2 = 40 | 100 | 600 | s = √(30² + 40²) / 2 = √2500 / 2 = 25; P = 4 × 25 = 100; A = ½ × 30 × 40 = 600 | |
| Rhombus | d1 = 20, d2 = 48 | 104 | 480 | s = √(20² + 48²) / 2 = √2704 / 2 = 26; P = 4 × 26 = 104; A = ½ × 20 × 48 = 480 | |
| Rhombus | d1 = 14, d2 = 48 | 100 | 336 | s = √(14² + 48²) / 2 = √2500 / 2 = 25; P = 4 × 25 = 100; A = ½ × 14 × 48 = 336 | |
| Rhombus | d1 = 24, d2 = 32 | 80 | 384 | s = √(24² + 32²) / 2 = √1600 / 2 = 20; P = 4 × 20 = 80; A = ½ × 24 × 32 = 384 | |
| Rhombus | d1 = 10, d2 = 6 | 23.3238 | 30 | s = √(10² + 6²) / 2 = √136 / 2 ≈ 5.831; P = 4s ≈ 23.3238; A = ½ × 10 × 6 = 30 | |
| Rhombus | d1 = 8, d2 = 4 | 17.8885 | 16 | s = √(8² + 4²) / 2 = √80 / 2 ≈ 4.4721; P = 4s ≈ 17.8885; A = ½ × 8 × 4 = 16 | |
| Rhombus | d1 = 12, d2 = 5 | 26 | 30 | s = √(12² + 5²) / 2 = √169 / 2 = 6.5; P = 4 × 6.5 = 26; A = ½ × 12 × 5 = 30 | |
| Rhombus | d1 = 10, d2 = 10 | 28.2843 | 50 | s = √(10² + 10²) / 2 = √200 / 2 ≈ 7.0711; P = 4s ≈ 28.2843; A = ½ × 10 × 10 = 50 | |
| Rhombus | d1 = 14, d2 = 8 | 32.249 | 56 | s = √(14² + 8²) / 2 = √260 / 2 ≈ 8.0623; P = 4s ≈ 32.249; A = ½ × 14 × 8 = 56 | |
| Rhombus | d1 = 20, d2 = 10 | 44.7214 | 100 | s = √(20² + 10²) / 2 = √500 / 2 ≈ 11.1803; P = 4s ≈ 44.7214; A = ½ × 20 × 10 = 100 | |
| Rhombus | d1 = 16, d2 = 12 | 40 | 96 | s = √(16² + 12²) / 2 = √400 / 2 = 10; P = 4 × 10 = 40; A = ½ × 16 × 12 = 96 | |
| Rhombus | d1 = 9, d2 = 12 | 30 | 54 | s = √(9² + 12²) / 2 = √225 / 2 = 7.5; P = 4 × 7.5 = 30; A = ½ × 9 × 12 = 54 | |
| Rhombus | d1 = 15, d2 = 20 | 50 | 150 | s = √(15² + 20²) / 2 = √625 / 2 = 12.5; P = 4 × 12.5 = 50; A = ½ × 15 × 20 = 150 | |
| Rhombus | d1 = 7, d2 = 24 | 50 | 84 | s = √(7² + 24²) / 2 = √625 / 2 = 12.5; P = 4 × 12.5 = 50; A = ½ × 7 × 24 = 84 | |
| Rhombus | d1 = 5, d2 = 12 | 26 | 30 | s = √(5² + 12²) / 2 = √169 / 2 = 6.5; P = 4 × 6.5 = 26; A = ½ × 5 × 12 = 30 | |
| Regular Hexagon | s = 1 | 6 | 2.5981 | P = 6 × 1 = 6; A = (3√3 / 2) × 1² ≈ 2.5981 | |
| Regular Hexagon | s = 2 | 12 | 10.3923 | P = 6 × 2 = 12; A = (3√3 / 2) × 2² ≈ 10.3923 | |
| Regular Hexagon | s = 3 | 18 | 23.3827 | P = 6 × 3 = 18; A = (3√3 / 2) × 3² ≈ 23.3827 | |
| Regular Hexagon | s = 4 | 24 | 41.5692 | P = 6 × 4 = 24; A = (3√3 / 2) × 4² ≈ 41.5692 | |
| Regular Hexagon | s = 5 | 30 | 64.9519 | P = 6 × 5 = 30; A = (3√3 / 2) × 5² ≈ 64.9519 | |
| Regular Hexagon | s = 6 | 36 | 93.5307 | P = 6 × 6 = 36; A = (3√3 / 2) × 6² ≈ 93.5307 | |
| Regular Hexagon | s = 7 | 42 | 127.3057 | P = 6 × 7 = 42; A = (3√3 / 2) × 7² ≈ 127.3057 | |
| Regular Hexagon | s = 8 | 48 | 166.2769 | P = 6 × 8 = 48; A = (3√3 / 2) × 8² ≈ 166.2769 | |
| Regular Hexagon | s = 9 | 54 | 210.4442 | P = 6 × 9 = 54; A = (3√3 / 2) × 9² ≈ 210.4442 | |
| Regular Hexagon | s = 10 | 60 | 259.8076 | P = 6 × 10 = 60; A = (3√3 / 2) × 10² ≈ 259.8076 | |
| Regular Hexagon | s = 12 | 72 | 374.123 | P = 6 × 12 = 72; A = (3√3 / 2) × 12² ≈ 374.123 | |
| Regular Hexagon | s = 15 | 90 | 584.5671 | P = 6 × 15 = 90; A = (3√3 / 2) × 15² ≈ 584.5671 | |
| Regular Hexagon | s = 20 | 120 | 1039.2305 | P = 6 × 20 = 120; A = (3√3 / 2) × 20² ≈ 1039.2305 | |
| Regular Hexagon | s = 25 | 150 | 1623.7976 | P = 6 × 25 = 150; A = (3√3 / 2) × 25² ≈ 1623.7976 | |
| Regular Hexagon | s = 30 | 180 | 2338.2686 | P = 6 × 30 = 180; A = (3√3 / 2) × 30² ≈ 2338.2686 | |
| Regular Hexagon | s = 50 | 300 | 6495.1905 | P = 6 × 50 = 300; A = (3√3 / 2) × 50² ≈ 6495.1905 | |
| Regular Hexagon | s = 100 | 600 | 25980.7621 | P = 6 × 100 = 600; A = (3√3 / 2) × 100² ≈ 25980.7621 | |
| Regular Hexagon | s = 0.5 | 3 | 0.6495 | P = 6 × 0.5 = 3; A = (3√3 / 2) × 0.5² ≈ 0.6495 | |
| Regular Hexagon | s = 2.5 | 15 | 16.238 | P = 6 × 2.5 = 15; A = (3√3 / 2) × 2.5² ≈ 16.238 | |
| Regular Hexagon | s = 7.5 | 45 | 146.1418 | P = 6 × 7.5 = 45; A = (3√3 / 2) × 7.5² ≈ 146.1418 |
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Frequently Asked Questions
| Question | Answer |
|---|---|
| What is the difference between perimeter and area? | Perimeter is the total length around the edge of a shape, measured in units such as cm. Area is the surface inside the shape, measured in square units such as cm². |
| What is the area formula for a trapezoid? | A = ½ × (a + b) × h, where a and b are the parallel sides and h is the height between them. For a = 12, b = 6, h = 4: A = ½ × 18 × 4 = 36. |
| How do you find the perimeter of a parallelogram? | P = 2(a + b), where a and b are the two different side lengths. Do not use the height. For b = 10 and a = 6: P = 2 × 16 = 32. |
| How do you find the area of a rhombus from its diagonals? | A = ½ × d1 × d2. For diagonals 10 and 6, A = ½ × 10 × 6 = 30. All four sides are equal, so the perimeter is 4s. |
| Why does a parallelogram use base times height, not base times side? | Area depends on the perpendicular height, not the slanted side. Slicing off a triangle and moving it turns the parallelogram into a rectangle of size b × h. |
| What is the area of a regular hexagon? | A = (3 × √3 / 2) × s², which is about 2.598 × s². For s = 6, A is about 93.5307 and the perimeter is 6 × 6 = 36. |