Mathematics
(a) The diagonals of a rhombus are 24 cm and 10 cm. Calculate its area and perimeter.
(b) The diagonals of a field in the form of a quadrilateral are 106 m and 80 m and intersect each other at right angles. Find the cost of cultivating the field at the rate of ₹ 25.50 per 100 m2.
Mensuration
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Answer
(a)

Let ABCD be the rhombus with diagonals AC and BD measuring 24 cm and 10 cm, respectively. We know that the diagonals of a rhombus bisect each other at right angles.
Area of rhombus = x (Product of diagonals)
= x 24 x 10
= x 240
= 120 cm2
Applying the Pythagorean theorem in Δ ADE:
AD2 = AE2 + DE2
= 122 + 52
= 144 + 25
= 169
AD =
= 13 cm
Perimeter of the rhombus = 4 x side
= 4 x 13
= 52 cm
Hence, the area of the rhombus is 120 cm2 and the perimeter is 52 cm.
(b) When the diagonals of a quadrilateral intersect at right angles, the area can be found using the formula:
Area of the quadrilateral = x d1 x d2
= x 106 x 80
= x 8480
= 4240 m2
Given that the cost of cultivation is ₹ 25.50 per 100 m2.
=
= ₹ 1081.20
Hence, the total cost of cultivation is ₹ 1081.20.
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