Question

ABC is scalene triangle base and height is 6m and 4m respectively. if the sector of radius 2m are cut from triangle then find the area of remaining portion​

Answer 1

Answer:

area of traingle=1/2×base×height

1/2×6×4

6×2

12cm²

area of sectorA=πr²∅1st/360⁰------Eq(I)

area of sector B=πr²∅2nd/360⁰-----(ii)

area of sector C=πr²∅3rd/360⁰----(iii)

area of shaded region=area of traingle-area of three sector

12cm-(πr²∅1st/360⁰ +πr²∅2nd/360+πr²∅3rd/360⁰)

12-{πr²/360 (∅1st+∅2nd +∅3rd)

(by taking πr²/360 common)

but we see that ∅1st,∅2nd and ∅3rd is also the angle of traingle and we know that sum of all angles of ∆=180⁰

12 - {πr²/(∅1st+∅2nd+∅3rd)}/360

12-{22/7 ×2²(180⁰)}/360⁰

12- {22/7 ×2×2×1}/2

12- {22/7×2}

12-44/7

(84-44)/7

40/7

5.714cm²

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