In Fig. 15.79, OCDE is a rectangle inscribed in a quadrilateral of a circle of radium 10 cm. If OE=2 , find the area of the rectangle.
Answers
Given : OCDE is a rectangle inscribed in a quadrilateral of a circle of radius 10 cm and OE = 2√5 cm.
[Mistake in the question]
We have :
Radius = OD = 10 cm and OE = 2√5 cm
In right ΔDEO,
By using Pythagoras theorem :
H² = P² + B²
OD² = OE² + DE²
(10)² = (2√5)² + DE²
100 = 4 × 5 + DE²
100 – 20 = DE²
DE² = 80
DE² = 16 × 5
DE = √16 × 5
DE = 4√5
Length of a rectangle , DE = 4√5 cm
Now,
Area of rectangle OCDE , A = Length x Breadth
A = DE × OE
A = 4√5 × 2√5
A = 4 × 2 × √5 × √5
A = 8 × 5
A = 40 cm²
Hence, Area of the rectangle is 40 cm².
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Answer:-
Given :
OCDE is a rectangle inscribed in a quadrilateral of a circle of radius 10 cm and OE = 2√5 cm.
[Mistake in the question]
We have :
Radius = OD = 10 cm and OE = 2√5 cm
In right ΔDEO,
By using Pythagoras theorem :
H² = P² + B²
OD² = OE² + DE²
(10)² = (2√5)² + DE²
100 = 4 × 5 + DE²
100 – 20 = DE²
DE² = 80
DE² = 16 × 5
DE = √16 × 5
DE = 4√5
Length of a rectangle , DE = 4√5 cm
Now,
Area of rectangle OCDE , A = Length x Breadth
A = DE × OE
A = 4√5 × 2√5
A = 4 × 2 × √5 × √5
A = 8 × 5
A = 40 cm²
Hence, Area of the rectangle is 40 cm².
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