Question

Find the area of a triangle of sides 5 cm, 12 cm and 13 cm.​

Answer 1

Verifying the sides by pythagoras theorem we see, this forms a right triangle with the right angle between the sides of 5cm and 12cm, i.e, they are the altitude and base of the triangle; so the area is given by (5*12)/2 =30cm²

Answer 2

★ Given:-      

• Side a = 5 cm
• Side b = 12 cm
• Side c = 13 cm

★ To find:-      

• The area of the triangle

★ Calculations:-          

Semi-perimeter:

• Semi-perimeter = a + b + c/2
• Semi-perimeter = 5 + 12 + 13/2
• Semi-perimeter = 30/2
• Semi-perimeter = 15 cm

. ° . The semi-perimeter is 15 cm.

                       ____________

Area of the triangle:

• Area of the triangle = √ s ( s - a ) ( s - b ) ( s - c )
• Area of the triangle = √ 15 ( 15 - 5 ) ( 15 - 12 ) ( 15 - 13 )
• Area of the triangle = √ 15 ( 10 ) ( 3 ) ( 2 )
• Area of the triangle = √ 15 × 10 × 3 × 2
• Area of the triangle = √ 900
• Area of the triangle = 30 cm²

. ° . The area of the triangle is 30 cm².

                              ___________