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.
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