Question

find the area of each of the following shaded region ​

Answer 1

Breadth=5.66m

Length:

Draw a line from the centre (radius) to form a triangle ∆OAB

Now ∆OAB is an isosceles triangle (both the sides are the radius of the circle)

therefore, OA=OB=4M

Now to find base:

drop a perpendicular OS from the centre

now this perpendicular is half of breadth=5.66/2=2.83m

therefore,OS=2.83m

• now AS = (4)²=(2.83)² + (AS)²
• 16=8.0089+(As)²
• 16 - 8.0089=AS²
• √7.9911=AS²
• AS=2.82
• Now Base AB=2(AS)
• THEREFORE, Base AB=2*2.82= 5.64
• Now area of rectangle=length*breadth
• 5.64 * 5.66=31.9224 m²

Answer 2

Answer:

Name the Rectangle as ABCD from top left side clockwise. Name the centre as O.

Join OB to form Right Angled ∆BCD

by Pythagoras law:

BD²= BC² + CD²

(4+4)²= (5.66)² + CD²

8²-5.66² = CD²

64-32.03 = CD²

32(approx.) = CD²

√32 = CD

CD = 5.66m

Area of circle = πr²

= 22/7 × (4)²

= 22×8/7

= 176/7

= 25 m² ( approx. )

Area of square = a²

= (5.66)²

= 32.033 m²

= 32m² ( approx. )

Therefore area of shaded portion =

32m²-25m²

= 7m²