Math, asked by michaeljohnjohn85, 9 months ago

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Answered by Anonymous
4

 \huge \mathbb \fcolorbox{black}{aqua}{ANSWER}

↝ Area of shaded region = Area of semi circle - Area of ∆PQR

↝ As QR is diameter , it forms semicircle .

↝ As we know angle in the semicircle is right angle . Hence , ∠RPQ is 90°

↝ Therefore , ∆PQR is right angled triangle

By Pythagoras Theorem

{(Hypotenuse)}^{2} = {(Base)}^{2} + {(Height)}^{2}

 {(QR)}^{2} = {(PR)}^{2} + {(PQ)}^{2}

 {(QR)}^{2} = {(24)}^{2} + {(7)}^{2}

 {(QR)}^{2} = 576 + 49

 {(QR)}^{2} = 625

↝ QR = √625

↝ QR = 25 cm

↝ Diameter of the circle = QR = 25 cm

↝ Radius = \frac{25}{2}

↝ Area of semicircle = \frac{1}{2} × π {r}^{2}

↝ Area of semicircle = \frac{1}{2}×\frac{22}{7} × \frac{25}{2} × \frac{25}{2}

↝ = \frac{11 × 25 × 25 }{28}

↝ = \frac{6875}{28}

↝ Area of semicircle = \frac{6875}{28}

_____________________________________

In ∆PQR

↝ Area of ∆PQR = \frac{1}{2} × base × height

↝ = \frac{1}{2} × PQ × PR

↝ = \frac{1}{2} × 24 × 7

↝ Area of ∆ PQR = 84 {cm}^{2}

_______________________________________

Area of shaded region = Area of semicircle - Area of ∆ PQR

↝ = \frac{6875}{28} - 84

↝ = \frac{6875 - 84 × 28}{28}

↝ = \frac{4523}{28}

↝ Area of shaded region = \frac{4523}{28} {cm}^{2}

_______________________________________

<marquee>✯✯ Hope It Helps✯✯

Answered by JUSTLIKETIGER
2

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