Page 131 - NUMINO Challenge_C1

15 Perimeter and Area of Figures

Basic Concepts Perimeter and Area in Rectangles

As the difference between the width and length of a rectangle becomes
smaller, the area of the rectangle with a fixed perimeter becomes greater.
Out of all the rectangles below that have a perimeter of 16 cm, the one
with the greatest area (16 cm2) is a square.

5 cm 4 cm
4 cm
1 cm 7 cm 3 cm
Area :7 cm2 Area :16 cm2

Area :15 cm2

As the difference between the width and length of a rectangle becomes
smaller, the perimeter of the rectangle with a fixed area becomes smaller.
Out of all the rectangles below that have an area of 36 cm2, the one with
the smallest perimeter (24 cm) is a square.

18 cm 9 cm 6 cm
Perimeter: 40 cm 6 cm
2 cm 4 cm
Perimeter:24 cm
Perimeter:26 cm

Example There are 35 sticks, each with a length of 1 cm. Explain how to
make a rectangle that has the greatest area using these sticks.
((Horizontal length) (Vertical length))

Class Notes

The perimeter of a rectangle is {(Width) (Length)} 2. So, the perimeter of a rectangle

cannot be an odd number. Therefore, you can use a maximum of sticks.

Because the area of a rectangle with a fixed perimeter increases as the difference

between the width and length becomes (smaller, greater), using sticks, you

should make the difference between the width and length the (smallest, greatest).

In other words, if you make a rectangle by putting sticks horizontally, and

vertically, it will have the greatest area. Therefore, the area is cm2.

128 NUMINO Challenge C1