find the area of each of the following shaded region
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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
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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
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