(1) From the measures given in the figure alongside, find the area of Δ ABC.

(2) Using Pythagoras’ theorem find the length of side AC.

(3) Find the area of Δ ABC using Heron’s formula.

(1) Given:

AB = 12 cm

BC = 5cm

Area of Δ ABC =

Area of Δ ABC = 30 sq cm

(2) According to pythagoras’ theorem:

AB² + BC² = AC²

⇒ AC² = 12² + 5²

⇒ AC = 13 cm

(3) Length of one side of the triangle (a) = 5 cm

Length of second side of the triangle(b) = 12 cm

Length of third side of the triangle (c) = 13 cm

Semi perimeter (s) =

According to Heron’s formula

Area of the triangle = √(s(s-a)(s-b)(s-c))

⇒ Area of the triangle = 30 sq cm