A right angled isosceles triangle is inscribed in a semi-circle

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A right angled isosceles triangle is inscribed in a semi-circle of radius 7 cm. The area enclosed by the semi-circle but exterior to the triangle is

1. 14 cm²
2. 28 cm²
3. 44 cm²
4. 68 cm²

Correct Option: B

Using Rule 1 and 14,

∠ACB = 90°
AC = CB = x cm
AB = 14 cm
From ∆ ABC
AC² + BC² = AB²
⇒ x² + x² = 142
⇒ 2x² = 14 × 14
⇒ x² = 14 × 7
⇒ x = √17 × 7 = 7√2cm
∴ Area of ∆ ABC

=	1	× AC × BC
	2

=	1	× 7√2 × 7√2 = 49 sq.cm.
	2

Area of semi-circle

=	πr²	=	22	× 7 × 7
	2		7 × 2

= 77 sq. cm
∴ Area of the shaded region = 77 – 49 = 28 sq. cm
= 28 cm²