Prove that the Area of a Rhombus is Equal to Half the Rectangle Contained by Its Diagonals. - Mathematics

Advertisements
Advertisements
Sum

Prove that the area of a rhombus is equal to half the rectangle contained by its diagonals.

Advertisements

Solution


Since the diagonals of a rhombus intersect at right angles,
Therefore, OB ⊥ AC and OD ⊥AC
Now, ar(rhombus ABCD)
= ar(ΔABC) + ar(ΔADC)

= `(1)/(2)("AC" xx "BO") + (1)/(2)("AC" xx "DO")`

= `(1)/(2){"AC" xx ("BO" + "DO")}`

= `(1)/(2)("AC" xx "BD")`

Therefore, the area of a rhombus is equal to half the rectangle contained by its diagonals.

  Is there an error in this question or solution?
Chapter 21: Areas Theorems on Parallelograms - Exercise 21.1

APPEARS IN

Frank Class 9 Maths ICSE
Chapter 21 Areas Theorems on Parallelograms
Exercise 21.1 | Q 21
Share
Notifications



      Forgot password?
Use app×