ShapesProperties
- Opposite sides are equal and parallel.
- Every angle is 90°.
- The diagonals are equal and cut each other in half.
- It has two lines of symmetry.
- A square is a rectangle whose length and breadth are equal.
Why the formulas work
A rectangle 6 cm long and 4 cm wide holds 4 rows of 6 unit squares, 24 in all. That is why area is length times breadth. Going round the edge you walk a length, a breadth, a length and a breadth: twice the sum. The diagonal is the hypotenuse of a right-angled triangle whose legs are the length and the breadth.
Worked example
Take a rectangle with length 15 cm and breadth 8 cm.
- Area. Area = l × b. Here: 15 × 8 = 120 cm².
- Perimeter. Perimeter = 2(l + b). Here: 2 × (15 + 8) = 46 cm.
- Diagonal. Diagonal = √(l2 + b2). Here: √(15² + 8²) = 17 cm.
Finding a missing measurement
Divide the area by the side you know: an area of 96 cm² and a length of 12 cm give a breadth of 8 cm. From the perimeter, halve it and take away the known side: a perimeter of 46 cm and a length of 15 cm give a breadth of 23 − 15 = 8 cm.
Mistakes to avoid
- Adding length and breadth gives half the perimeter, not the area.
- Both sides must be in the same unit before multiplying. Change 2 m and 50 cm to 200 cm and 50 cm first.
- Two rectangles can have the same perimeter and different areas, and the other way round.
Where you see it
Books, doors, phone screens, cricket pitches, plots of land and most rooms are rectangles. Flooring, painting and fencing sums are nearly always rectangle sums.
Try these
Work each one out, then tap to check.
A rectangle has length 24 cm and breadth 7 cm. Find its area, perimeter and diagonal.
Area = 168 cm²; Perimeter = 62 cm; Diagonal = 25 cm.
A rectangle has length 12.5 cm and breadth 6 cm. Find its area, perimeter and diagonal.
Area = 75 cm²; Perimeter = 37 cm; Diagonal = 13.87 cm.