□ PQRS is a rhombus. If QR =30,
PR=36 and the point of intersection
of diagonals PR and QS is T.
Find the area of the rhombus PQRS.
Answers
Given : PQRS is a rhombus.
QR =30, PR=36 and the point of intersection of diagonals PR and QS is T.
To Find : the area of the rhombus PQRS.
Solution:
Diagonals of rhombus bisect each other perpendicularly
PR = 36 cm
=> RT = 36/2 = 18 cm
QR = 30 cm
ΔQTR is right angle at T
Pythagoras' theorem: square on the hypotenuse of a right-angled triangle is equal to the sum of the squares of the other two perpendicular sides.
QR² = QT² + RT²
=> 30² = QT² + 18²
= QT² = 30² - 18²
=> QT² = (30 + 18)(30 - 18)
=> QT² = 48 x 12
=> QT² = 12 x 4 x 12
=> QT = 12 x 2
=> QT = 24 cm
Hence diagonal QS = 2 * 24 = 48 cm
Area of rhombus = (1/2) * diagonal 1 * diagonal 2
= (1/2) * 36 * 48
=36 * 24
= 864
area of the rhombus PQRS. = 864 sq units
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