Question

Find the area of the shaded region of each figure

Answer 1

Answer (1) :---

it is given that, a circle is inside a Square of side 5cm.

→ Remember :-- Diameter of circle inside a square = side of square .

So, Diameter of Circle = 5 cm

→ radius of circle = (5/2)cm .

→ Area of circle = πr² = π*(5/2)² = 25π/4 cm²

And, Area of square = (side)² = 5² = 25cm² .

Hence,

Area of shaded region = Area of square - Area of circle = 25 - (25π/4) = (100-25π)/4 = 25(4-π)/4 cm² (Ans).

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Answer (2) :----

→ Given that diameter of bigger circle = 12cm.

When we do shifting we can easily see that,

Area of shaded region = Semi - circle Area with centre O1 + Semicircle Area with centre O2.

or,

→ Shaded Area = π(r1)²/2 + π(r2)²/2

→ shaded Area = (π/2)( r1² + r2²)

Now, with given data , we cant find shaded area . ( we can use (a²+b² = (a+b)² - 2ab ) but we dont have value of r1*r2.

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Answer (3) :------

→ Shaded Area = Area of square - Area of 1 circle with diameter is Equal to side of square )

( Logic :--- 4 Quadrant make a full circle )

So,

→ Shaded Area = (21)² - π(21/2)² = 441 - (441π/4) = 441(1-π/4) cm²

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Answer (4) :----

→ shaded Area = Area of Rectangle - Area of one semi-circle ..

→ Shaded area = length * Breadth - (πr²)/2

→ shaded Area = 50*140 - (π*7²)/2

→ shaded Area = 50*7*10*2 - π*7*7/2

→ shaded Area = 7(1000 - 7π/2)

→ shaded Area = 7(1000-11)

→ shaded area = 6923cm²

( Sides are not clearly visible sorry if calculation is not correct) . But method is correct..

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Answer (5) :---

→ shaded Area = Area of big circle with diameter (14+7)cm - [ Area of circle with diameter 14cm + Area of circle with diameter 7cm ]

→ Shaded Area = π(21/2)² - [ π*7² + π(7/2)² ]

→ shaded Area = π[ 441/4 - (49 + 49/4) ]

→ Shaded Area = π( 441/4 - 245/4)

→ shaded Area = π*196/4

→ shaded Area = 22/7 * 196/4

→ shaded Area = 11*28/2

→ shaded Area = 11*14

→ shaded Area = 154cm²

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Answer (6) :------

→ shaded Area = Area of big circle with diameter (8+7)cm - [ Area of semi- circle with diameter 8cm + Area of semi- circle with diameter 7cm ] ...

→ Shaded Area = π(15/2)² - [ π(4)²/2 + π(3.5)²/2 ]

→ shaded Area = π[ 225/4 - ( 8 + 6.125)

→ shaded Area = π(225/4 - 14.125)

→ shaded Area = π[(225-56.5)/4]

→ Shaded Area = π × (168.5/4)

→ shaded Area = 132.2725 cm²

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( Hope it Helps you ) ..