Page 132 - NUMINO Challenge_C1

Basic Concepts Diagonals and Area in Rhombuses

In each rhombus below, the sum of the two diagonals is 12.

1 BC
1A

The differences between the lengths of the diagonals of rhombuses A, B,
and C are 8, 4, and 0 respectively; and the areas are 10, 16, and 18
respectively. As you can see, the area of each rhombus with a fixed sum of
the lengths of the two diagonals becomes greater as the difference between
the lengths of the two diagonals becomes smaller.

Example Find the greatest area of the quadrilateral which has 9 cm as the
sum of the lengths of the two diagonals. (The lengths of the
diagonals are natural numbers.)

Class Notes

The area of a quadrilateral with two fixed diagonals is the (smallest, greatest) when the

diagonals meet perpendicularly.

In a quadrilateral with perpendicular diagonals, the total area becomes greater as the

difference between the lengths of the diagonals becomes (smaller, greater).

Therefore, the lengths of the diagonals should be cm and cm each.

Therefore, when the diagonals meet , and are cm

and cm each, the area of the quadrilateral is 2 cm2.

4 cm 4 cm 5 cm
5 cm 5 cm 4 cm

129Measurement