Area of a rhombus is equal to __________ of its diagonals
Solution:
The area of a rhombus can be expressed as half the product of its diagonals.
✦Try This: If L is the length of the side of the rhombus ABCD as shown below, then demonstrate that the area of the rhombus is half the product of the diagonals.
The properties of a rhombus which are used here are:
1) The four sides of the rhombus are equal
2) The length of the diagonals are unequal
3) The diagonals bisect each other at right angles.
4) OA = OC and OB = OD
Let OA = OC = y
OB = OD = x
Area of △AOB = △BOC = △COD = △DOA = ½(x)(y)
The area of the Rhombus = sum of the areas of the four triangle = 4 × (½)(x)(y) = 2xy (1)
Length of one Diagonal = 2x
Length of the other diagonal = 2y
Half of the product of the two diagonals is = (½)(2X)(2Y) = 2xy (2)
Since (1) = (2) it is proved that the area of a Rhombus is equal to half the product of its diagonals
☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11
NCERT Exemplar Class 8 Maths Chapter 11 Sample Problem 3
Area of a rhombus is equal to __________ of its diagonals
Summary:
Area of a rhombus is equal to half the product of its diagonals
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