Question

In adjoining figures ABC is a quadrant of a circle of radius 14cm and a semi circle is drawn with BC as diameter find the area of shaded region.

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Answer 1

Step-by-step explanation:

given :

• ABC = quadrant of a circle of radius 14cm

• semi circle is drawn with BC as diameter find the area of shaded region.

to find:

• the area of shaded region. = ?

• the area of shaded region = ?

solution :

shaded region =semicircle diameter

semicircle diameter = 1/2 π r

diameter = 1/2 x 22/7 x 7√2 x 7√2

• right angle of hypotenuse = 14 or 14√2 = 2 ×

• r = 7√2] = 11 x 7 x 2 = 154 cm

quadrant area = 1/4 πr

• area = 1/4 x 22/7 × 14 × 14 = 22 x 7 = 154

• traingle area = 1/2 × h× b

• traingle = 1/2 x 14 x 14 = 98 cm

• shaded region = 154 - 98 = 98

hence, the answer is 98

Answer 2

$\huge\tt\color{cyan}{Answer}$

Area of shaded region = Area of semicircle of diameter BC-{area of quadrant of radius AB /AC - area of ∆ABC }

So, area of semicircle of diameter BC = $\sf{\dfrac{1}{2} \pi^2}$

$\rm :\longmapsto{\frac{1}{2} × \frac{22}{7} × 7\sqrt{2} × 7\sqrt{2}}$

[ ∵ BC is hypotenuse of right angle ∆ABC , here AB = BC = 14 so, BC = 14√2 = 2 × radius ⇒ radius = 7√2 ]

= 11 × 7 × 2 = 154 cm²

Area of quadrant of radius AB/AC = $\sf{\dfrac{1}{4} \pi^2}$

$\rm :\longmapsto{\frac{1}{4} × \frac{22}{7} × 14 × 14}$

= 22 × 7 = 154 cm²

Area of ∆ABC = 1/2 × height × base

= 1/2 × 14 × 14 = 98 cm²

Now, area of shaded region = 154cm² {154cm² - 98cm²} = 98cm²

Hence, area of shaded region = 98 cm²

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