Question

The side of a square is 10cm. The area of circumscribed and inscribed circles is

_________.

(a) 157 cm2, 78.5cm2 (b) 150 cm2, 75cm2 (c) 147 cm2, 78.5cm2 (d) 157 cm2,

79.5cm2​

Answer 1

Step-by-step explanation:

Area=π×5×5=25πcm

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Answer 2

Answer:

(a) 157cm^2, 78.5cm^2

Step-by-step explanation:

1) Circumscribed-(the circle outside of the square but touching the corner of square)

first we need to find the diameter which is the hypotenuse of the triangle formed by the square of side 10cm

so Height = 10cm

    Base    =10cm

    Hypotenuse = ??

    the angle between Height and Base is 90°

 by pythagoras theorem                Height² + Base² = Hypotenuse²

i.e 10²+10² = hypo.²

     200=hypo.²

 hypo = √200

           = 10√2 =  diameter

r=d÷2

r = 5√2

so the area of circumscribed circle is         πr²

                                                                  = 22÷7 × (5√2)²

                                                                 = 22÷7 x 25 x 2

                                                                 = 22÷7 ×50

                                                                  by solving u get 157 cm²

Inscribed- (circle inside the square touching the inside of square at midmoing of the side )

the diameter is the side of the square which is 10 cm

then r = 5cm

so area = πr² = 22÷7 x 5²  

                       =22÷7 × 25

                       = by solving further we get 78.5 cm²

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