Q3 of 16 Page 153

The area of a rhombus is 216 square centimetres and the length of one of its diagonals is 24 centimetres. Compute the following measurements of this rhombus.

i) Length of the second diagonal


ii) Length of a side


iii) Perimeter


iv) Distance between sides

Length of a diagonal (d1) = 24 cm

Area of the rhombus = 216 cm2


Area of the rhombus = × d1 × d2


× d1 × d2 = 216


d1 × d2 = 432


24 × d2 = 432


d2 = 18 cm


(i) length of another diagonal = 18 cm



We can see that some part of the rhombus constitutes a right-angle triangle.


From that


H2 = 92 + 122


H = √225


= 15


(ii)∴ side of a rhombus is 15 cm


We know that sides are equal in a rhombus


(iii) So, perimeter = 4 × sides


= 4 × 15


= 60 cm


(iv) In rhombus distance between the side is also a side


∴ distance between the side is 15 cm


More from this chapter

All 16 →
1

Draw a square of area square centimetres.

2

Draw a non-square rhombus of area 9 square centimetres.

 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?