Question

in the given figure PQRS is a rectangle of length 10√2 breath 5√2cm if PEO is an isoscles triangle inscribed in the semi circle with diameter PQ then find the area of the shaded region​

Answer 1

Answer:

Area of shaded region = 200/7 $cm^{2}$

Step-by-step explanation:

As isoscles triangle is inserted in a semi circle, before that these both inserted in rectangle PQRS. therefore length of rectangle is equal to diameter of semi circle.

Radius = 5√2

Area = 1/2 pi r square

= 1/2*22/7*5√2*5√2 = 550/7 sq. cm

Now, breadth of rectangle can be taken as height of triangle.

Therefore, area of triangle = 1/2 base height

= 1/2 * 5√2 * 10√2 = 50 sq. cm

Area of shaded region = 550/7-50

= 200/7  sq. cm  

Answer 2

Answer:

200/7 sq. cm

Step-by-step explanation:

Radius = 5√2

Area = 1/2 pi r square

= 1/2*22/7*5√2*5√2 = 550/7 sq. cm

Now, breadth of rectangle can be taken as height of triangle.

Therefore, area of triangle = 1/2 base height

= 1/2 * 5√2 * 10√2 = 50 sq. cm

Area of shaded region = 550/7-50

= 200/7 sq. cm