Question

Find the area of the figure with Heron’s formula

Answer 1

735 cm²

Explanation:

The figure is a trapezium .The area of the triangle section can be calculated using the Heron's formula.

The other part of the figure will be a square of sides 21 cm by 21 cm

Area of the square section

Area = l²

Area = 21* 21 = 441 cm²

Area of the triangle using Heron's formula

Sides of the triangle are ;

a= 28 cm

c= 35 cm

b = 21 cm -----height of the trapezium

The Heron's formula is given as;

`A=√(s( s-a)(s-b )(s-c ))`

where s is half the perimeter of the triangle

Perimeter of the triangle is given as ;

P= 35 + 28 + 21 =84 cm

s= 84/2 = 42 cm

`A=√(42*(42-21 )*(42-35 )*(42-28 )) \\\\A=√(42*(21 )*(7 )*( 14)) \\\\A=√(86436) \\\\A=294\\\\`

Total area = 294 + 441 = 735 cm²