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In figure find the area of the red part.​

In figure find the area of the red part.​-example-1
User Guy Blanc
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2 Answers

4 votes
The first one is correct
User Leanna
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4 votes

Explanation:

Given : A rectangle 4 x 8 , a semicircle

Diagonal intersecting semicircle

To Find :Area of red part

Solution:

Angle AC make AB α = ∠BAC

tan α = BC/AB = 4/8 = 1/2

=> α = 26.565°

∠ECA = ∠BAC = α

EC = EF = 4

=> ∠CEF = 180° - 2α

∠AED = 45° as AE is diagonal of Square of side 4

=> ∠AEF + 180° - 2α + 45° = 180°

=> ∠AEF = 2α - 45° = 8.13°

in Left side area between square and circle is split in 2 Equal parts

(1/2) area - area AFG = area of Red part

in Left side area between square and circle = 4² - (1/4)π4²

= 3.4336 sq unit

half = 1.7168 sq unit

Now find area AFG = area ΔAEF - sector EGF

area ΔAEF

AE = 4√2 , EF = 4 angle = 8.13°

area ΔAEF = (1/2) 4√2 * 4 sin 8.13° = 1.6 sq unit

area sector EGF = (8.13/360)π4² = 1.135 sq unit

area AFG = 1.6 - 1.135 = 0.465 sq unit

Area of Red part = 1.7168 - 0.465 sq unit

= 1.2518 sq unit

= 1.252 sq unit

= 1.25 sq unit.

Hope this helps!!

In figure find the area of the red part.​-example-1
User Davejlin
by
8.5k points

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