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With vertices A,B and C of a triangle ABC as centres, arcs are drawn with 5cm each. With sides AB=14cm, BC=48cm and CA =50cm, find Area of whole triangle minus the sum of the three sectors

given ABC is a triangle such that AB=14 cm, BC=48cm, CA=50 cm

length of the radius =5cm

area of the circle with radius 5 =

area of the sector through A=.........(1)

area of the sector through B=.........(2)

area of the sector through C=.........(3)

siince sum of the interior angles of the triangle is 180 deg.

......(4)

from (1), (2) and (3) and (4)

sum of the areas of the sectors from A, B and C=

area of the triangle by heron's formula:

where s is the semi-perimeter of the triangle.

here a=48 cm, b=50 cm and c=14 cm,

area of the triangle ABC =

area of the triangle - sum of the three sectors =336-39.25=296.75 sq cm

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