Q6 of 16 Page 153

What is the area of the largest rhombus that can be drawn inside a rectangle of sides 6 centimetres and 4 centimetres?

We have to draw largest rhombus inscribed in rectangle.

Rectangle breadth (b) = 6cm


Height (h) = 4 cm


We know that in rhombus is directly proportional to the diagonals of it.


In a rectangle we can’t draw diagonals more than its height and breadth.


So, the largest diagonals are height, breadth of rectangle


∴ the area of rhombus = × ×


= × ×


= × ×


= 3 cm2


A rhombus with area of 3 is largest possible in rectangle 6 × 4


More from this chapter

All 16 →
4

A 68-centimeter-long rope is used to make a rhombus on the ground. The distance between a pair of opposite corners is 16 meters.

i) What is the distance between the other two corners?


ii) What is the area of the ground bounded by the rope?

 5

In the figure, the midpoints of the diagonals of a rhombus are joined to form a small quadrilateral:


(i) Prove that this quadrilateral is a rhombus.


(ii) The area of the small rhombus is 3 square centimetres. What is the area of the large rhombus?

 1

What is the area of the quadrilateral shown below?

 2

Prove that for any quadrilateral with diagonals perpendicular, the area is half the product of the diagonals.