Question

5. Find the area of the triangle formed by the points by using Heron's formula.
1) (1, 1), (1, 4) and (5, 1)
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Answer 1

Answer:

6 cm sq.

Step-by-step explanation:

A right angled triangle will be formed.

See IMAGE :-

AC= 3 cm AB= 4cm

By Pythagoras Therom:-

AC sq. + AB sq. = BC sq.

(3 cm) sq. + (4 cm) sq. = BC sq.

9 sq + 16 cm sq = BC sq.

Root 25 cm sq = BC

BC = 5cm

By heron's Formula :-

s = AB+BC+AC /2

s= 3cm + 4 cm + 5 cm /2

s= 6 cm

Area of triangle = Root s(s-a)(s-b)(s-c)

= Root 6cm ( 6cm-3cm)(6cm-4cm)(6cm-5cm)

= Root 6cm × 3cm × 2cm × 1 cm

= Root 2 cm × 3cm × 3cm × 2 cm

= 2 cm × 3 cm

= 6 cm sq.