Question

#similar isosceles triangles and congruent right angled triangles in a semicircle of radius = 1 unit. find the total shaded area.

Geometry_Puzzle

Answer 1

Answer:

19

$∆ \: ABC \: is \: a \: right \: angled \: triangle \: . \: \\ So, \: by \: Pythagoras \: theorem \\ {AC}^{2} = {AB}^{2} + {BC}^{2} = {7}^{2} + {7}^{2} = 98 \\ = AC = \sqrt{98} = 7 \sqrt{2} cm \\ arc \: A - B - C \: is \: a \: semicircle$

Answer 2

$\huge{\underline{\mathtt{\red{A}\pink{N}\green{S}\blue{W}\purple{E}\orange{R}}}}$

▽ABC is a right angled triangle.

so by Pythagoras theorem

AC² = AB²+ BC² = 7²+7² = 98

= AC= $\sqrt{98}$ = 7$\sqrt{2}$