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# find the area of the shaded region if abcd is a rectangle with sides 8cm and 6cm

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### Mohammed

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## Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. [CBSE 2014]

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. [CBSE 2014]

Areas of Different Plane Figures

Find the area... Question

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle. [CBSE 2014]

Open in App Solution

In right triangle ABC

AC2 = AB2 + BC2 = 82 +62 = 64 + 36 = 100 ∴ AC2 = 100 ⇒ AC = 10 cm

=12AC=5cm

Area of the shaded region = Area of circle − Area of rectangle OABC

π π =πOA2-AB×BC =227×52-8×6 =78.57-48 =30.57cm2

Hence, the area of the shaded region is 30.57 cm2.

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SIMILAR QUESTIONS

Q.

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.

Q. In the given figure, ABCD is a rectangle with AB = 80 cm and BC = 70 cm, ∠AED = 90° and DE = 42 cm. A semicircle is drawn, taking BC as diameter. Find the area of the shaded region. [CBSE 2014]

Q. If the inner rectangle is 8cm x 6 cm, find the area of the shaded region. (Given that the centre of circle and rectangle is same)Q. In the given figure, find the area of the shaded region, where ABCD is a square of side 14 cm and all circles are of the same diameter. [CBSE 2014]

Q. In the given figure, O is the centre of the circle with AC = 24 cm, AB = 7 cm and ∠BOD = 90°. Find the area of shaded region.

[Use π = 3.14] [CBSE 2012]

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## Find the area of the shaded region if ABCD is a rectangle with sides 8 cm and 6 cm and O is the center of circle. (Take pi = 3.14)

Click here👆to get an answer to your question ✍️ Find the area of the shaded region if ABCD is a rectangle with sides 8 cm and 6 cm and O is the center of circle. (Take pi = 3.14)

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>>Find the area of the shaded region if AB

Question

## Find the area of the shaded region if ABCD is a rectangle with sides 8cm and 6cm and O is the center of circle.(Takeπ=3.14)

Given sides of rectangle is l=8 cm,b=6 cm

Medium Open in App Solution Verified by Toppr From the figure

Diameter of circle is equal to Diagonal of rectangle

⟹radius= 2 1 ​ 6 2 +8 2 ​ =5 cm

Area of circle is πr

2 =π(5) 2 =25π=78.5cm 2

Area of rectangle is l×b=6×8=48 cm

2

Area of shaded portion = Area of Circle − Area of Rectangle

=78.5−48=30.5 cm 2

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## Find the Area of the Shaded Region in the Given Figure, If Abcd is a Rectangle with Sides 8 Cm and 6 Cm and O is the Centre of the Circle.

Find the Area of the Shaded Region in the Given Figure, If Abcd is a Rectangle with Sides 8 Cm and 6 Cm and O is the Centre of the Circle.

Find the area of the shaded region in the given figure, if ABCD is a rectangle with sides 8 cm and 6 cm and O is the centre of the circle.

### SOLUTION

In right triangle ABC

AC2 = AB + BC2 = 82 + 62 = 64 + 36 = 100 ∴ AC2 = 100 ⇒  AC = 10 cm

Area of the shaded region = Area of circle − Area of rectangle OABC

OAABBC ⇒π(OA)2-AB×BC ⇒227×(5)2-8×6 = 78.57 - 48 = 30.57 cm2

Hence, the area of the shaded region is 30.57 cm2.

Concept: Area of Circle

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Chapter 18: Area of Circle, Sector and Segment - Exercise 18A [Page 823]

Q 43 Q 42 Q 44

### APPEARS IN

RS Aggarwal Secondary School Class 10 Maths

Chapter 18 Area of Circle, Sector and Segment

Exercise 18A | Q 43 | Page 823

2018-2019 (March) 30/1/3 (with solutions)

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Mohammed 9 day ago

Guys, does anyone know the answer?