65
Perimeter of irregular shapes
Textbook: Part 2, lesson 65, pp. 81–83
GoalPerimeter of irregular shapes: the sum of all sides and rectangles with a cut corner.
New words
polygon · ko‘pburchakcut corner · kesik burchaklength · uzunlikgoing around · o‘rab chiqish
Explanation
The perimeter of any polygon is the sum of the lengths of all its sides. If a smaller rectangle is cut from the corner of a rectangle, the new shape has the same perimeter as the original rectangle: the two new sides at the cut make up for the sides that were removed.
Worked examples
A pentagon with sides 5, 7, 4, 6, 8 cm has perimeter 5 + 7 + 4 + 6 + 8 = 30 cm.
A 10 cm × 10 cm square is cut from the corner of a 30 cm × 20 cm rectangle. The perimeter does not change: 2 × (30 + 20) = 100 cm.
Class activity
“Cut the corner”: children draw a rectangle on squared paper, cut a piece from a corner and compare the perimeter before and after.
Practice
1
A quadrilateral has sides 12 m, 9 m, 15 m and 7 m. Find its perimeter.
43
2
A 30 m × 20 m rectangle is cut from the corner of a 120 m × 80 m field. How many metres of wall are needed around the remaining shape?
400
3
A staircase-shaped figure is made by cutting steps out of one corner of a 10 dm × 6 dm rectangle (the steps use only horizontal and vertical segments). What is its perimeter in dm?
32
4
A triangle has perimeter 120 cm and two sides of 35 cm and 48 cm. How long is the third side, in cm?
37