Question

CBSE CLASS X

CIRCLES - MATHEMATICS

Answer 1

Now,AB=13 cm
AC=12 cm

Since ABC is a right triangle,
[AC + BC]square = AB square
144 + BC square = 169
BC square = 25
BC = 5 cm

Since AB is the diameter,
Area of Shaded region = Area of 1/2 triangle - Area of triangle ABC

Area of 1/2 circle = 1/2 * 3.14 * 6.5 * 6.5
= 66.3 cm sq.

Area of triangle = 1/2 * 5 * 12
= 30 cm sq.

Therefore.
Area of Shaded region = 66.3 - 30
= 36.3 cm sq.

HOPE IT HELPS :)

Answer 2

Area of the semicircle :

Area of semi-circle = 1/2 × π r²

Given :

r = diameter / 2

  = AB / 2

  = 13 / 2

Area = 1/2 × π × 13/2 × 13/2

        = 169/8 × π

        = 21.125 × π

Put the value of π :

         = 21.125 × 3.14

         = 66.325

The area of semi-circle is 66.325 cm²

Area of the triangle

Area of a triangle = 1/2 × base × height .

∠ACB = 90° [ ∠ subtended by a semi-circle ]

So : By Pythagoras theorem :-

AB² = AC² + BC²

==> BC² = AB² - AC²

             = 13² - 12²

             = 169 - 144

             = 25

==> BC² = 25

So BC = 5 cm

Area = 1/2 × BC × AC

        = 1/2 × 5 × 12

        = 5 × 6

        = 30

Area of Δ ABC = 30 cm²

Area of the shaded region

Area of shaded region = area of semi-circle - area of Δ ABC

                                      = 66.325 cm² - 30 cm²

                                      = 36.325 cm²

$\textsf{\underline{\huge{ANSWER}}}$

The area of the shaded region is 36.325 cm².

Hope it helps !

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