Question

Find the area of a rhombus having each side equal to 13 cm and one of its diagonals 10 centimetre

Answer 1

Let PQRS be a rhombus whose side is 13cm . Let the diagonal PR and QS intersect each other at T. Let QS measure 10cm .
The diagonals of a Rhombus bisect each other at right angles and angle PTQ is a right angle.
In ∆PTQ using Pythagoras theorem:
= PT^2 + QT^2 = PQ^2
= PT^2 + 5^2 = 13^2
= PT^2 + 25 = 169
= PT^2 = 169 - 25 = 144
= PT^2 = 12cm
PR = 2 x PT
= 2 x 12 = 24cm
Area of a Rhombus = 1/2 x d1 x d2
= 1/2 x 24 x 10
= 120cm^2.

Answer 2

Answer:

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