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

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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]

Byju's Answer Standard X Mathematics

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

Now, Radius of circle(OA)

=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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Areas of Different Plane Figures

Standard X Mathematics

## 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 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 cmMedium 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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In the given figure, ABCD is a square of side 5 cm inscribed in a circle. Find the area of the shaded region104 12 SIMILAR QUESTIONS [Take π=3.14]

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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.

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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.

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### 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

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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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